All
the publications are available by request: BorisovDI@yandex.ru
Some articles can be downloaded online.
The links starting from arXiv or
from mp_arc are to the freely accessible prepints.
The links indicated asjournal are to the full-texts
in journal. You may need subscription to access these texts.
Articles
167. D.I. Borisov, D.M. Polyakov. Spectral asymptotics for one-dimensional Schroedinger operator on segment with translation in free term and Dirichlet condition // submitted.
166. D.I. Borisov, D.M. Polyakov. Asymptotics for eigenvalues of Schroedinger operator with small translation and Dirichlet condition // submitted.
165. D.I. Borisov, D.M. Polyakov. Uniform spectral asymptotics for Schroedinger operator on segment with delta-interaction // submitted.
164. D.I. Borisov. Geometric approximation of point interactions in three-dimensional domains // Mathematics. 2024. V. 12. No. 7. id 1031.
journal
163. D.I. Borisov, A.L. Piatnitski and E.A. Zhizhina. Non-local convolution type operators with potential: essential and infinite discrete spectrum // submitted.
162. D.I. Borisov, R.R. Suleimanov. Operator estimates for problems in domains with singular curved boundary: Dirichlet and Neumann conditions // Doklady Mathematics. 2024, to appear.
161. D.I. Borisov and A.A. Fedotov. Monodromization and a PT-symmetric nonself-adjoint quasi-periodic operator // Russian Journal of Mathematical Physics. 2023. V. 30. No. 3. P. 294-309. journal
160. D.I. Borisov, R.R. Suleimanov. On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with fast oscillating boundaries // Mathematical Notes, to appear.
159.D.I. Borisov, R.R. Suleimanov. On operator estimates for elliptic equations in multi-dimensional domains with a strongly curved boundary // Sbornik Mathematics, to appear.
158. D.I. Borisov, A.L. Piatnitski and E.A. Zhizhina. Spectrum of one-dimensional potential perturbed by a small convolution operator: general structure // Mathematics. 2023. V. 11. No. 19. id 4042.
journal
157. D.I. Borisov, D.M. Polyakov. Resolvent convergence for differential-difference operators with small variable translations // Mathematics. 2023. V. 11. No. 20. id 4260.
journal
156. G. Berkolaiko, D.I. Borisov, M. King. Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge // Analysis and Mathematical Physics. 2023. V. 13. id 90.
arXiv:2308.06362journal
155. D.I. Borisov, D.A. Zezyulin. Eigenvalues bifurcating from continuum in two-dimensional potentials generating non-Hermitian gauge fields // Annals of Physics. 2023. V. 459. id 169498. arXiv:2310.12549journal
154. D.I. Borisov. On resolvent of the Schrödinger operator on a model graph with small loops // Journal of Mathematical Sciences. 2023. V. 276. No. 1. P. 48-60.
journal
153. D.I. Borisov, D.A. Zezyulin. On perturbation of thresholds in essential spectrum under the coincidence of virtual level and spectral singularity // Russian Journal of Mathematical Physics. 2024. V. 31. No. 1. P. 60-78.
journal
152. D.I. Borisov. Geometric approximation of point interactions in two-dimensional domains for non-self-adjoint operators // Mathematics. 2023. V. 11. No. 4. id 947.
журнал
151. D.I. Borisov. Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case // Ufa Mathematical Journal. 2022. V. 14. No. 4. C. 26-41. journal
150. D.I. Borisov. Operator estimates in two-dimensional problem with a frequent alternation in the case of small parts with the Dirichlet condition // Proceedings of Steklov Institute of Mathematics. 2023. V. 321. Suppl. 1. P. S33-S52.
journal
149. D.I. Borisov. Homogenization of operators with perturbations of general form in the lower-order terms // Mathematical Notes. 2023. V. 113. No. 1-2. P. 138--142.
журнал
148. D.I. Borisov. Operator estimates for non-periodically perforated domains: disappearance of cavities // Applicable Analysis. 2024. V. 103. No. 5. P. 859-873. arXiv:2210.12749journal
147. S.V. Dmitriev and D.I. Borisov. Effective interatomic potential for modelling shock waves in carbon nanotube bundles // AIP Conference Proceedings. 2022. V. 2533. id 020005.
journal
146. D.I. Borisov, M. N. Konyrkulzhaeva. Operator L2-estimates for two-dimensional problems with frequent alternation of boundary conditions // Journal of Mathematical Sciences. 2022. V. 267. No. 3. P. 319--337. journal
145. D.I. Borisov. Homogenization for operators with arbitrary perturbations of coefficients // Journal of Differential Equations. 2023. V. 369. P. 41-93. arXiv:2205.09490journal
144. D.I. Borisov, A.A. Fedotov. On Bloch solutions of difference Schrödinger equations // Functional Analysis and its Applications. 2022. V. 56. No. 4. P. 3--16.
журнал
143. D.I. Borisov. Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term // Mathematical Models in the Applied Sciences. 2024. V. 47. No. 6. P. 4122-4164. arXiv:2205.09490журнал
142. D. I. Borisov, L. I. Gazizova. Taylor series for resolvents of operators on graphs with small edges // Proceedings of Steklov Institute of Mathematics. 2022. V. 317. Suppl. 1. P. S37--S54.
journal
141. D.I. Borisov. Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions // Journal of Mathematical Sciences. 2022. V. 264. No. 5. P. 562--580. journal
140. M. Znojil, D. Borisov. Arnold’s potentials and quantum catastrophes II // Annals of Physics. 2022. V. 442. id 168896.
arXiv:2101.02015journal
139. D.I. Borisov, J. Kříž. Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit // Analysis and Mathematical Physics. 2023. V. 13. id. 5. arXiv:2204.04829журнал
138. D.I. Borisov, A.I. Mukhametrakhimova. Asymptotics for problems in perforated domains with nonlinear Robin condition on boundaries of cavities // Sbornik Mathematics. 2022. V. 213. No. 10. P. 1318--1371.
journal
137. D.I. Borisov, A.I. Mukhametrakhimova. Norm resolvent convergence for problems with perforation alogn a given manifold and with a nonlinear Robin condition on the boundaries of cavities // Saint-Petersburg Mathematical Journal. 2024. V. 35. No. 4, to appear.
arXiv:2202.10767
136. D.I. Borisov. Norm resolvent convergence of elliptic operators in domains with thin spikes // Journal of Mathematical Sciences. 2022. V. 261. No. 3. P. 366--391. journal
135. D.I. Borisov, A.L. Piatnitski, E.A. Zhizhina. On spectra of convolution operators with potentials // Journal of Mathematical Analysis and Applications. 2023. V. 517. No. 1. id 126568. arXiv:2201.04511journal
134. D.I. Borisov, A.L. Piatnitski, E.A. Zhizhina. Spectrum of a convolution operator with potential // Russian Mathematical Survey. 2022. V. 77. No. 3. P. 546--548.
journal
133. D.I. Borisov, A.A. Fedotov. On spectrum of non-self-adjoint quasiperiodic operator // Doklady Mathematics. 2021. V. 104. No. 3. P. 326--331. journal
132. D.I. Borisov, D.A. Zezyulin. On bifurcations of thresholds in essential spectrum under presence of spectral singularity // Differential Equations. 2023. V. 59. No. 2. P. 278--282.
journal
131. D.I. Borisov. Spectra of elliptic operators on quantum graphs with small edges // Mathematics. 2021. V. 9. No. 16. id. 1874. journal
130. D.I. Borisov and D.A. Zezyulin. Bifurcations of essential spectra generated by a small non-Hermitian small hole. II. Eigenvalues and resonances // Russian Journal of Mathematical Physics. 2022. V. 29. No. 3. P. 321-341.
journal
129. D.I. Borisov and D.A. Zezyulin. Bifurcations of essential spectra generated by a small non-Hermitian hole. I. Meromorphic continuations // Russian Journal of Mathematical Physics. 2021. V. 28. No. 4. P. 416--433. journal
128. D.I. Borisov, M. N. Konyrkulzhaeva, A. I. Mukhametrakhimova. On discrete spectrum of a model graph with loop and small edges // Journal of Mathematical Sciences. 2021. V. 257. No. 5. P. 3-18. journal
127. D.I. Borisov. Quantum graphs with small edges: holomorphy of resolvents // Doklady Mathematics. 2021. V.103. No. 3. P. 113-117. journal
126. D.I. Borisov. Analyticity of resolvents of elliptic operators on quantum graphs with small edges // Advances in Mathematics. 2022. V. 397. id 108125. arXiv:2102.12958journal
125. I.R. Sunagatova, A.M. Subkhangulova, M.N. Semenova, A.S. Semenov, D.I. Borisov and S.V. Dmitriev. Properties of one-dimensional nonlinear vibrational modes in triangular lattice with Lennard-Jones interactions // IOP Conference Series: Materials Science and Engineering. 2020. V. 1008. id 012073. journal
124. A.M. Bayazitov, E.A. Korznikova, A.S. Semenov, D.I. Borisov and S.V. Dmitriev. Interaction of supersonic 2-crowdions in fcc platinum // IOP Conference Series: Materials Science and Engineering. 2020. V. 1008. id 012068. journal
123. D.I. Borisov. Asymptotic analysis of boundary value problems for Laplace operator with frequent alternation of boundary conditions // Journal of Mathematical Sciences. 2023. V. 277. No. 6. P. 841--958. journal
122. D.I. Borisov, M.N. Konyrkulzhayeva. On infinite system of resonances and eigenvalues with exponential asymptotics generated by distant perturbations // Ufa Mathematical Journal. 2020. V. 12. No. 4. P. 3-18. journal
121. D.I. Borisov, A.M. Golovina. On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders // Journal of Mathematical Analysis and Applications. 2021. V. 496. No. 2. id 124809. arXiv:2008.07289journal
120. D.I. Borisov, P. Exner. Approximation of point interactions by geometric perturbations in two-dimensional domains // Bulletin of Mathematical Sciences. 2023. V. 13. No. 2. id 2250003. arXiv:2008.00478journal
119. D.I. Borisov, A.I. Mukhametrakhimova. On a model graph with a
loop and small edges // Journal of Mathematical Sciences. 2020. V. 251. No. 5. P. 573-601.
journal
118. D.I. Borisov, D.A. Zezyulin, M. Znojil. Bifurcations of
thresholds in essential spectra of elliptic operators under
localized non-Hermitian perturbations // Studies in Applied Mathematics. 2021. V. 146. No. 4. P. 834-880. arXiv:2007.02258journal
117. D.I. Borisov, O.A. Sultanov. Complete asymptotics for
solution of singularly perturbed dynamical systems with single
well potential // Mathematics. 2020. V. 8. No. 6. id 949. journal
116. M. Znojil, D. Borisov. Anomalous mechanisms of the loss of
observability in non-Hermitian quantum models // Nuclear Physics
B. 2020. V. 957. id 115064. arXiv:2005.13069journal
115. D.I. Borisov, G. Cardone, G.A. Chechkin, Yu.O. Koroleva.
On elliptic operators with Steklov condition perturbed by
Dirichlet condition on a small part of boundary // Calculus of Variations and Partial Differential Equations. 2021. V. 60. No. 1. id 48. journal
114. D.I. Borisov, M. Täufer, I. Veselić. Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum // Journal of Statistical Physics. 2021. V. 182. No. 1. id. 1. arXiv:2003.03562journal
113. D.I. Borisov, A.I. Mukhametrakhimova. Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition // Sbornik Mathematics. 2021. V. 212. No. 8. P. 1068-1121. journal
112. D.I. Borisov, A.M. Golovina, A.I. Mukhametrakhimova. Analytic continuation of resolvent of analytic continuation in cylinder // Journal of Mathematical Sciences. 2020. V. 250. No. 2. P. 260-284. journal
111. D.I. Borisov. On elliptic operators with frequent alternation of boundary conditions along a given curve // Journal of Mathematical Sciences. 2020. V. 244. No. 3. P. 378-389. journal
110. D.I. Borisov, O.A. Sultanov. Asymptotic analysis of exit time for dynamical systems with a single well potential // Journal of Differential Equations. 2020. V. 269. No. 8. P. 78-116. arXiv:1906.04715journal
109. D.I. Borisov, D.A. Zezyulin. Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials // Applied Mathematical Letters. 2020. V. 100. id 106049. arXiv:1908.06384journal
108. D.I. Borisov, D.A. Zezyulin. Spacing gain and absorption in a simple PT-symmetric model: spectral singularities and ladders of eigenvalues and resonances // Journal of Physics A: Mathematical and Theoretical. 2019. V. 52. No. 44. id 445202. arXiv:1908.06383journal
107. D.I. Borisov, M.N. Konyrkulzhayeva. Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge // Journal of Mathematical Sciences. 2019. V. 239. No. 3. P. 248-267. journal
106. D.I. Borisov, M.N. Konyrkulzhayeva. Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum // Ufa Mathematical Journal. 2019. V. 11. No. 2. P. 56-70. journal
105. D.I. Borisov, P. Exner. Gap opening in two-dimensional periodic systems // Communications in Contemporary Mathematics. 2021. V. 23. No. 1. id 1950080. arXiv:1810.08824journal
104. D.I. Borisov. Bethe-Sommerfeld conjecture for periodic Schroedinger operators in strip // Journal of Mathematical Analysis and Applications. 2019. V. 479. No. 1. P. 260-282. arXiv:1806.09292journal
103. D.I. Borisov. On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a band with oscillating boundary // Journal of Mathematical Sciences. 2021. V. 257. No. 3. P. 273-285. journal
102. D.I. Borisov , A.M. Golovina. On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with distant perturbation // Journal of Mathematical Sciences. 2021. V. 258. No. 1. P. 1--12. journal
101. D.I. Borisov, M. Täufer, I. Veselić. Spectral localization for quantum Hamiltonians with weak random delta interaction // Comptes Rendus Mathématique. 2018. V. 356. No. 6. P. 686-691. journal
100. M. Znojil, D. Borisov. Two patterns of PT- symmetry breakdown in a non-numerical six-state simulation // Annals of Physics. 2018. V. 394. P. 40-49. arXiv:1804.07324journal
99. D.I. Borisov. On gaps in spectrum of Laplacian in strip with a periodic delta interaction // Proceedings of Steklov Institute of Mathematics. 2020. V. 305. Suppl. 1. P. S16-S23. journal
98. D.I. Borisov, A.I. Mukhametrakhimova. On norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes // Journal of Mathematical Sciences. 2018. V. 232. No. 3. P. 283-298. journal
97. D.I. Borisov. On gaps in the lower part of the spectrum of a periodic magnetic operator in a strip // Journal of Mathematical Sciences. 2021. V. 253. No. 5. P. 599-617.
journal
96. D.I. Borisov. Perturbations of the continuous spectrum of a certain nonlinear two-dimensional operator sheaf // Journal of Mathematical Sciences. 2021. V. 252. No. 2. P. 135-146. journal
95. D.I. Borisov. On absence of gaps in a lower part of spectrum of Laplacian with frequent alternation of boundary conditions in strip // Theoretical and Mathematical Physics. 2018. V. 195. No. 2. P. 690-703. journal
94. D.I. Borisov. On spectral gaps of a Laplacian in a strip with a bounded periodic pertutbation // Ufa Mathematical Journal. 2018. V. 10. No. 2. P. 14-30. journal
93. D.I. Borisov. Initial length scale estimate for the Schroedinger operator with a random fast oscillating potential in a multi-dimensional layer // KazNU Bulletin. Mathematics, Mechanics, Computer Science Series. 2017. V. 93. No. 1. P. 21-31.
92. D. Saadatmand, D.I. Borisov, P.G. Kevrekidis, K. Zhou, S.V. Dmitriev. Resonant interaction of φ4 kink with spatially periodic PT -symmetric perturbation // Commnications in Nonlinear Science and Numerical Simulation. 2018. V. 56. P. 62-76. journalarXiv:1611.08281
91. D.I. Borisov. Initial length scale estimate for layers with small random negative definite perturbations // Journal of Mathematical Sciences. 2019. V. 241. No. 5. P. 518-548. journal
90. D.I. Borisov, M. Znojil. On eigenvalues of a PT- symmetric operator in a thin layer // Sbornik Mathematics. 2017. V. 208. No. 2. P. 173-199. journal
89. D. Borisov, G. Cardone. On a one-dimensional quadratic operator pencil with a small periodic perturbation // ESAIM: Control, Optimisation and Calculus of Variations. 2020. V. 26. id 21. journal
88. D. Borisov, F. Hoecker-Escuti, I. Veselić. Expansion of the spectrum in the weak disorder regime for random operators in continuum space // Communications in Contemporary Mathematics. 2018. V. 20. No. 1. id 1750008. journal
87. D. Borisov, R.K. Gaydukov. Existence of the stationary solution of a Rayleigh-type equation // Mathematical Notes. 2016. V. 99. No. 5. P. 636-642. journal
86. D. Borisov, M. Tautenhahn, I. Veselić. Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations // Journal of Mathematical Physics. 2017. V. 58. No. 12. id 121502. arXiv:1512.06347journal
85. D. Borisov, S. Dmitriev. On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation // Studies in Applied Mathematics. 2017. V. 138. No. 3. P. 317-342. arXiv:1512.01103journal
84. D. Borisov, M. Tautenhahn and I. Veselić . Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators // in "Mathematical Results in Quantum Mechanics". Proceedings of the QMath12 Conference. 2014. P. 89-99. journal
83. D. Borisov, I. Nakić, C. Rose, M. Tautenhahn and I. Veselić. Multiscale unique continuation properties of eigenfunctions // in "Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics". Operator Theory: Advances and Applications. Birkhauser. V. 250. 2015. P. 107-118. journal
82. D.I. Borisov, T.F. Sharapov. On resolvent on multi-dimensional operators with frequent alternation of boundary condition in the case of Robin homogenized boundary condition // Journal of Mathematical Sciences. 2016. V. 213. No. 4. P. 3-40. journal
81. D. Borisov, M. Znojil. Mathematical and physical meaning of the crossings of energy levels in PT- symmetric systems // in "Non-Hermitian Hamiltonians in Quantum Physics", Springer Proceedings in Physics. 2016. P. 201-217. arXiv:1303.4876journal
80. D. Borisov. Creation of spectral bands for a periodic domain with small windows // Russian Journal of Mathematical Physics. 2016. V. 23. No. 1. P. 19-34. arXiv:1507.01169journal
79. D. Borisov. Perturbation of threshold of essential spectrum for waveguide with window. II. Asymptotics // Journal of Mathematical Sciences. 2015. V. 210. No. 5. P. 590-621. journal
78. D.I. Borisov, R.Kh. Karimov, T.F. Sharapov. Initial length scale estimate for waveguides with some random singular potentials // Ufa Mathematical Journal. 2015. V. 7. No. 2. P. 33-54. arXiv:1507.02235journal
77. D. Saadatmand, S.V. Dmitriev, D.I. Borisov, P.G. Kevrekidis, Minnekhan A. Fatykhov, K. Javidan. The effect of the φ4 kink's internal mode during scattering on PT-symmetric defect // JETP Letters. 2015. V. 101. No. 7. P. 497-502. arXiv:1411.5857journal
76. D. Borisov, A. Golovina, Ivan Veselić. Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate // Annales Henri Poincare. 2016. V. 17. No. 9. P. 2341-2377. arXiv:1501.06503journal
75. D. Borisov. Emergence of eigenvalue for PT- symmetric operator in thin strip // Mathematical Notes. 2015. V. 98. No. 6. P. 827-883. journal
74. D.I. Borisov, F. Ružička and M. Znojil. Multiply degenerate exceptional points and quantum phase transitions // International Journal of Theoretical Physics. 2015. V. 54. No. 12. P. 4293-4305. arXiv:1412.6634journal
73.D. Saadatmand, S.V. Dmitriev, D.I. Borisov, P.G. Kevrekidis, M.A. Fatykhov, K. Javidan. Kink scattering from a parity-time-symmetric defect in the ϕ4 model // Communications in Nonlinear Science and Numerical Simulation. 2015. V. 29. No. 1-3. P. 267-282. arXiv:1411.5857journal
72. D. Borisov, P. Freitas. The spectrum of geodesic balls on spherically symmetric manifolds // Communications in Analysis and Geometry. 2017. V. 25. No. 3. P. 507-544. arXiv:1603.02399journal
71. S.V. Suchkov, D.I. Borisov, A.A. Sukhorukov, Yu.S. Kivshar. Signal manipulation with a PT-symmetric coupler embedded into an array of optical waveguides // Letters on materials. 2014. V. 4. No. 4. P. 222-225. journal
70. D. Borisov. Perturbation of threshold of essential spectrum for waveguide with window. I. Decaying resonance solutions // Journal of Mathematical Sciences. 2015. V. 205. No. 2. P. 19-54. journal
69. D. Saadatmand, S.V. Dmitriev, D. Borisov, P.G. Kevrekidis. Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect // Physical Review E. 2014. V. 90. No. 5. id. 052902 (10 pp). journalarXiv:1408.2358
68. D. Borisov, F. Hoecker-Escuti, I. Veselić. Expansion of the almost sure spectrum in the weak disorder regime // Journal of Functional Analysis. 2016. V. 270. No. 5. P. 1684-1718. arXiv:1408.2113journal
67. D. Borisov, G. Cardone, T. Durante. Norm resolvent convergence for elliptic operators in domain with perforation along curve // Comptes Rendus Mathematique. 2014. V. 352. No. 9. P. 679-683. journal
66. D. Borisov. Eigenvalues collision for PT-symmetric waveguide // Acta Polytechnica. 2014. V. 54. No. 2. P. 93-100. journalarXiv:1401.6316
65. D. Borisov. On band spectrum of Schroedinger operator in periodic system of domains coupled by small windows // Russian Journal of Mathematical Physics. 2015. V. 22. No. 2. P. 153-160. arXiv:1312.7534journal
64. D. Borisov. Discrete spectrum of thin PT-symmetric waveguide // Ufa Mathematical Journal. 2014. V. 6, No. 1. P. 29-55. journalarXiv:1403.4524
63. D. Borisov, G. Cardone, T. Durante. Homogenization and uniform resolvent convergence for elliptic operators in a strip perforated along a curve // Proceedings of the Royal Society of Edinburgh, Section: A Mathematics. 2016. V. 146. No. 6. P. 1115-1158. arXiv:1305.1009journal
62. D.I. Borisov, K.V. Pankrashkin. Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones // Journal of Physics A: Mathematical and Theoretical. 2013. V. 46. No. 23. id 235203 (18 pp) arXiv:1211.5786journal
61. D. Borisov, I. Veselić. Low lying eigenvalues of randomly curved quantum waveguides // Journal of Functional Analysis. 2013. V. 265. No. 11. P. 2877-2909. arXiv:1211.1314journal
60. D. Borisov, P. Exner, A. Golovina. Tunneling resonances in systems without a classical trapping // Journal of Mathematical Physics. 2013. V. 54. No. 1. id 012102 (19 pp). arXiv:1210.0449mp_arc 12-106journal
59. D. Borisov, G. Cardone , L. Faella, C. Perugia. Uniform resolvent convergence for a strip with fast oscillating boundary // Journal of Differential Equations. 2013. V. 255. No. 12. P. 4378-4402. arXiv:1206.1771journal
58. D. Borisov, A. Golovina. On the resolvents of periodic operators with distant perturbaions // Ufa Mathematical Journal. 2012. V. 4. No. 2. P. 65-73. journal
57. D. Borisov, R. Bunoiu, G. Cardone. Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics // Zeitschrift fuer Angewante Mathematik und Physik. 2013. V. 64. No. 3. P. 439-472. arXiv:1203.0210journal
56. D. Borisov, G. Cardone. Planar waveguide with "twisted" boundary conditions: small width // Journal of Mathematical Physics. 2012. V. 53. No. 2. id 023503. arXiv:1112.1787journal
55. D. Borisov, K. Pankrashkin. Gaps opening and splitting of the zone edges for waveguides coupled by a periodic system of small windows // Mathematical Notes. 2013. V. 93. No. 5. P. 660-675. arXiv:1203.0201journal
54. D. Borisov, K. Pankrashkin . On extrema of band functions in periodic waveguides // Functional Analysis and its Applications. 2013. V. 47. No. 3. P. 238-240. journal
53. D. Borisov, G. Cardone. Planar waveguide with "twisted" boundary conditions: discrete spectrum // Journal of Mathematical Physics. 2011. V. 52. No. 12. id 123513. arXiv:1110.3452journal
52. D. Borisov. On the homogenization of Schroedinger operator in a strip with frequent alternation of boundary conditions // Bulletin of Chelyabinsk State University. Mathematics. Mechanics. Informatics. 2011. No. 27. P. 6-11 (in russian) journal
51. D. Borisov, P. Freitas. On the spectrum of deformations of compact double-sided flat hypersurfaces // Analysis and Partial Differential Equations. 2013. V. 6. No. 5. P. 1051-1088. journal
50. D. Borisov. On a PT-symmetric waveguide with a pair of small holes // Proceedings of Steklov Institute of Mathematics. 2013. V. 281. No. 1 supplement. P. 5-21. journal
49. D. Borisov, P. Freitas. Eigenvalues asymptotics for almost flat compact hypersurfaces // Doklady Mathematics. 2012. V. 85. No. 1. P. 18-22. journal
48. D. Borisov, R. Bunoiu, G. Cardone. Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows // Journal of Mathematical Sciences. 2011. V. 176. No. 6. P. 774-785. journal
47. D. Borisov, D. Krejčiřík .The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions // Asymptotic Analysis. 2012. V. 76. No. 1. P. 49-59. arXiv:1102.5051journal
46. D. Borisov, I. Veselić. Low lying spectrum of weak-disorder quantum waveguides // Journal of Statistical Physics. 2011. V. 142. No. 1. P. 58-77. arXiv:1010.0315journal
45. D. Borisov, R. Bunoiu, and G. Cardone. On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition // Annales Henri Poincare. 2010. V. 11. No. 8. P. 1591-1627. arXiv:1010.2072journal
44. D. Borisov, R. Bunoiu, and G. Cardone. On a waveguide with an infinite number of small windows // Comptes Rendus Mathematique. 2011. V. 349. No. 1-2. P. 53-56. journal
43. D. Borisov, I. Veselić. Spectral properties of weak-disorder quantum waveguides // Oberwolfach Reports. 2009. V. No. 4. P. 2980-2981. journalmirror
42. D. Borisov, and G. Cardone. Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional rods // ESAIM: Control, Optimisation, and Calculus of Variation. 2011. V. 17. No. 3. P. 887-908. arXiv:0910.3907journal
41. D. Borisov, P. Freitas. Asymptotics for the expected lifetime of Brownian motion on thin domains in Rn // Journal of Theoretical Probabilty. 2013. V. 26. No. 1. P. 284-309. arXiv:0909.5516journal
40. D. Borisov, I. Veselić. Spectral gaps for self-adjoint second order operators // Zeitschrift für Analysis und ihre Anwendungen . 2012. V. 31. No. 4. P. 473-505. arXiv:1010.0314journal
39. D. Borisov. On spectrum of two-dimensional periodic operator with small localized perturbation // Izvestia mathematics. 2011. V. 75. No. 3. P. 471-505. journal
38. D. Borisov, and G. Cardone. Homogenization of the planar waveguide with frequently alternating boundary conditions // Journal of Physics A: Mathematics and General. 2009. V. 42. No. 36, 365205 (21pp). arXiv:0905.0338journal
37. D. Borisov, and P. Freitas. Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in Rd // Journal of Functional Analysis. 2010. V. 258. No. 3. P. 893-912. arXiv:0908.2327journal
36. D. Borisov, and P. Freitas. Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation // Journal of Differential Equations. 2009. V. 247. No. 11. P. 3028-3039. arXiv:0905.3242journal
35. D. Borisov, and R. Gadyl'shin. A letter to editor // Sbornik Mathematics. 2008. V. 199. No. 3. P. 160. (in russian version only)
34. D. Borisov and P. Freitas. Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions on thin planar domains // Annales de l'Institut Henri Poincare (C) Analyse non-lineaire. 2009. V. 26. No. 2. P. 547-560. arXiv:0712.3245journal
33. D. Borisov. Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients // Proceedings of Steklov Institute of Mathematics. V. 2007, Suppl. 2. P. S35-S45. preprintjournal
32. D. Borisov, D. Krejčiřík . PT-symmetric waveguide // Integral Equations and Operator Theory. 2008. V. 62. No. 4. P. 489-515. arXiv:0707.3039journal
31. D. Borisov. The spectrum of two quantum layers coupled by a window // Journal of Physics A: Mathematical and Theoretical. 2007. V. 40. No. 19. P. 5045-5066. arXiv:math-ph/0702023journal
30. D. Borisov. Asymptotics for the solutions of elliptic systems with fast oscillating coefficients // St. Petersburg Mathematical Journal. 2009. V. 20. No. 2. P. 175-191. arXiv:math-ph/0612013journal
29. D. Borisov. On a quantum waveguide with a small PT-symmetric perturbation // Acta Polytechnica. 2007. No. 2-3. P. 59-61. journal
28. D.I. Borisov, R.R. Gadyl'shin. Spectrum of a periodic operator with a small localized perturbation // Doklady Mathematics. 2007. V. 75. No. 2. P. 255-259. journal
27. D. Borisov. Some singular perturbations of periodic operators // Theoretical and Mathematical Physics. 2007. V. 151. No. 2. P. 614-624. journal
26. D.I. Borisov, R.R. Gadyl'shin. On spectrum of periodic operator with a small localized perturbation // Izvestia mathematics. 2008. V. 72. No. 4. P. 659-688. arXiv:math.SP/0609195journal
25. D.I. Borisov. Distant perturbations of the Laplacian in a multi-dimensional space // Annales Henri Poincare. 2007. V. 8. No. 7. P. 1371-1399. arXiv:math-ph/0608006journal
24. D. Borisov and P. Exner. Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case // Journal of Mathematical Physics. 2006. V. 47. No. 11. P. 113502-1 - 113502-24. arXiv:math-ph/0606022mp_arc 06-177journal
23. D. Borisov. Asymptotic behaviour of the spectrum of a waveguide with distant perturbation // Mathematical Physics, Analysis and Geometry. 2007. V. 10. No. 2. P. 155-196. arXiv:math-ph/0606011journal
22. D.I. Borisov, R.R. Gadyl'shin. On spectrum of self-adjoint differential operator on the axis with fast oscillating coefficients // Sbornik Mathematics. 2007. V. 198. No. 8. P. 1063-1093. journal
21. D.I. Borisov, R.R. Gadyl'shin. On spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential // Theoretical and Mathematical Physics. 2006. V. 147. No.1. P. 496-500. arXiv:math-ph/0508013journal
20. D.I. Borisov. On the spectrum of a Schroedinger operator perturbed by a rapidly oscillating potential // Journal of Mathematical Sciences. 2006. V. 139. No. 1. P. 6243-6322. arXiv:math-ph/0505068journal
19. D.I. Borisov. Asymptotics for the spectrum of a Schroedinger operator perturbed by a fast oscillating periodic potential // Doklady Mathematics. 2006. V. 73. No. 1. P. 19-22. journal
18. D. Borisov. Discrete spectrum of a pair of non-symmetric waveguides coupled by a window // Sbornik Mathematics. 2006. V. 197. No. 4. P. 475-504. arXiv:math-ph/0512066journal
17. A. Bikmetov and D. Borisov. On the discrete spectrum of Schrodinger operator with a narrow well // Theoretical and Mathematical Physics. 2005. V. 145. No. 3. P. 1691-1702. journal
16. D. Borisov, T. Ekholm and H. Kovařík . Spectrum of the magnetic Schrodinger operator in a waveguide with combined boundary conditions // Annales Henri Poincare. 2005. V. 6. No. 2. P. 327-342. arXiv:math-ph/0405034journal
15. D. Borisov and P. Exner. Exponential splitting of bound states in a waveguide with a pair of distant windows // Journal of Physics A: Mathematics and General. 2004. V. 37. No. 10. P. 3411-3428. arXiv:math-ph/0312013mp_arc 03-525journal
14. D.I. Borisov. On a problem with nonperiodic frequent alternation of boundary condition imposed on fast oscillating sets // Computational Mathematics and Mathematical Physics. 2006. V. 46. No. 2. P. 271-281. arXiv:math-ph/0306052journal
13. D.I. Borisov. Asymptotics and estimates of the convergence rate in a three-dimensional boundary-value problem with rapidly alternating boundary conditions // Siberian Mathematical Journal. 2004. V. 45. No. 2. P. 222-240. arXiv:math-ph/0209021journal
12. D.I. Borisov. Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating nonperiodic boundary conditions // Izvestia Mathematics. 2003. V. 67. No. 6. P. 1101-1148. arXiv:math-ph/0209004journal
11. D. Borisov, P. Exner and R. Gadyl'shin. Geometric coupling thresholds in a two-dimensional strip // Journal of Mathematical Physics. 2002. V. 43. No. 12. P. 6265-6278. arXiv:quant-ph/0206113mp_arc 02-268journal
10. D.I. Borisov. On a model boundary value problem for Laplacian with frequently alternating type of boundary condition // Asymptotic Analysis. 2003. V. 35. No. 1. P. 1-26. arXiv:math-ph/0208009journal
9. D.I. Borisov. On a singularly perturbed boundary value problem for Laplacian in a cylinder // Differential Equations. 2002. V. 38. No. 8. P. 1140-1148. journal
8. D.I. Borisov. Boundary value problem in a cylinder with frequently changing type of boundary condition // Sbornik Mathematics. 2002. V. 193. No. 7. P. 977-1008. journal
7. D.I. Borisov. On a Laplacian with frequently nonperiodically alternating boundary conditions // Doklady Mathematics. 2002. V. 65. No. 2. P. 224-226. journal
6. D.I. Borisov. Two-parametrical asymptotics for the eigenevalues of the Laplacian with frequent alternation of boundary conditions // Vestnik Molodyh Uchenyh. Seriya Prikladnaya matematika i mehanika (Journal of young scientists. Applied mathematics and mechanics). 2002. No. 1. P. 36-52. (in Russian) journal
5. D.I. Borisov. The asymptotics for the eigenelements of the Laplacian in a cylinder with frequently alternating boundary conditions // Comptes Rendus Acad. Sci. Paris, Serie IIb. 2001. t. 329. No. 10. P. 717-721. journal
4. D. Borisov, P. Exner, R. Gadyl'shin and D. Krejčiřík . Bound states in weakly deformed strips and layers // Annales Henri Poincare. 2001. V. 2. No. 3. P. 553-572. arXiv:math-ph/0011052mp_arc 00-473journal
3. D.I. Borisov. Two-parameter asymptotics in a boundary-value problem for the Laplacian // Mathematical Notes. 2001. V. 70. No. 3/4. P. 471-485. journal
2. D.I. Borisov, R.R. Gadyl'shin. On the spectrum of the Laplacian with frequently alternating boundary conditions // Theoretical and Mathematical Physics. 1999. V. 118. No.3. P. 272-277. journal
1. D.I. Borisov, R.R. Gadyl'shin. On Laplacian with rapidly and quasiperiodically changing type of boundary conditions // Russian Mathematical Survey. 1998. V. 53. No. 4. P. 813. journal
Selected Conferences
63. Conference "Dynamics in Siberia", Novosibirsk, February 26 - March 2, 2024.
62. International Conference "Nonlocal and Nonlinear Problems", Moscow, October 23-28, 2023.
61. Workshop "Semiclassical Analysis and Nonlocal Elliptic Theory", Moscow, October 17-20, 2023.
60. International Scientific Conference "Ufa Autumn Mathematical School-2023", Ufa, October 4-8, 2023.
59. Conference "Partial differential equations and their applications" dedicated to 115th anniversary of S.L. Sobolev, Novosibirsk, October 2-4, 2023.
58. II All-Russian Scientific Practical Conference "Mathematics in Contemporary World", dedicated to 160th anniversary of outstanding Russian mathematician D.A. Grave, Vologda, September 19-23, 2023 г.
57. Annual International Conference "Day on Difraction-2023", Saint-Petersburg, June 5-9, 2023.
56. 14th St. Petersburg Conference in Spectral Theory dedicated to the memory of M.Sh.Birman, Saint-Petersburg, June 19-23, 2023.
55. Voronezh Spring Mathematical School "Pontryagin Readins"-2023, May 3-9, 2023.
54. Conference "Dynamics in Siberia", Novosibirsk, February 27 - March 4, 2023.
53. 2nd conference of Mathematical Centers of Russia, Moscow, November 7-11, 2022.
52. The 9th International Conference on Differential and Functional Differential Equations, Moscow, June 28-July 5, 2022.
51. 13th St. Petersburg Conference in Spectral Theory
dedicated to the memory of M.Sh.Birman, Saint-Petersburg, June 22-26, 2022.
50. International Conference "Complex analysis, Mathematical Physics and Nonlinear equations", South Ural, Yakty-Kul, March 14-18, 2022.
49. International Conference "Order Analysis And Related Problems Of Mathematical Modeling, XVI. Operator Theory And Differential Equations", Vladikavkaz, 20-24 September, 2021.
48. Pierre Duclos Workshop, Saint Petersburg, September 20-22, 2021.
47. Analytic and algebraic methods in physics XVIII, Doppler Institute microconference, Prague/Řež, September 1-3, 2021.
46. The International Workshop on Operator Theory and its Applications
(IWOTA-2021), Chapman University in Orange, USA. August 9-13, 2021.
45. 1st conference of Mathematical Centers of Russia, Sirius, August 9-13, 2021 г.
44. International conference "Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis-2021", Москва, 30 июня-9 июля 2021 г.
43. 12th St. Petersburg Conference in Spectral Theory
dedicated to the memory of M.Sh.Birman, Saint-Petersburg, June 23-26, 2021.
42. Annual International Conference "Day on Difraction-2021", Saint-Petersburg, May 31-June 4, 2021.
41. International Conference "Complex analysis, Mathematical Physics and Nonlinear equations", South Ural, Yakty-Kul, March 15-19, 2021.
40. International Conference "Spectral theory and related questions", Ufa, October 1-4, 2018.
39. The 8th International Conference on Differential and Functional Differential Equations, Moscow, August 13-20, 2017.
38. International conference of the theory of functions dedicated to centenary of A.F. Leontiev, Ufa, May 24-27, 2017.
37. Trilateral German-Russian-Ukrainian Summer School "Spectral Theory, Differential Equations and Probability", Mainz, September 4-15, 2016.
36. Ufa International mathematical conference, Ufa, September 27-30, 2016.
35. The Conference of Professors of RAS, Moscow, June 14-16, 2016.
34. International conference "Waveguides: asymptotic methods and numerical analysis", Naples, May 21-23, 2015.
33. Annual International Conference "Day on Difraction-2015", St. Peterburg, May 25-29 , 2015.
32. The Seventh International Conference on Differential and Functional Differential Equations, Moscow, August 22-29, 2014.
31. International Conference "Nonlinear Equations and Complex Analysis", Bannoe, March 17-21, 2014.
30. 5th St.Petersburg conference in Spectral Theory dedicated to the memory of M.Sh.Birman, St.-Petersburg, July 2-6, 2013.
29. International conference "Nonlinear analysis and spectral problems", Ufa, June 18-22, 2013.
28. Trilateral French-German-Russian Workshop "Asymptotic analysis and spectral theory on non-compact structures", Mainz, September 10-12, 2012.
27. International school-seminar "Nonlinear analysis and spectral problems", Ufa, April 4-5, 2012
26. International Conference "Spectral theory and its applications" in memory of A.G.Kostychenko, Ufa, June 13-15, 2011
25. All-Russian conference "Asymptotical methods in the theory of differential equations", Chelyabinsk, June 7-12, 2011
24. Internation conference "Differential Equations and Related Topics" dedicated to Ivan G. Petrovskii, Moscow, May 29-June 4, 2011
23. International conference "Multiscale methods and qualitative properties for differential operators " on the occations of V.V. Zhikov 70th birthday, Neapol, May 6-7, 2011.
22. International conference "QMath 11 - Mathematical Results in Quantum Physics", Hradec Kralove, September 5-10, 2010.
21. Annual International Conference "Day on Diffraction-2010", St. Petersburg, June 8-11, 2010.
20. Mini-Workshop "Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence", Oberwolfach, December 6-12, 2009.
19. XVIth International Congress on mathematical physics, Prague, August 3-8, 2009.
18. International Conference ''Differential Equations and Dynamical Systems'', Suzdal, June 27 - July 2, 2008.
17. Workshop "Perturbed periodic PDE, problems with singular boundaries, and their numerical aspects", Cardiff, September 25-26, 2007.
16. 3rd Walkshop "Operators, Spectra and Mathematical Physics", Goettingen, June 29, 2007.
15. International Symposium "Operator Theory in Quantum Physics", Prague, September 10-14, 2006.
14. Workshop "Spectral Theory and its Applications", Cambridge, July 24-28, 2006.
13. 21st Max Born Symposium "Mathematical Problems in Nonrelativistic Quantum Dynamics", Wroclaw, June 26-28, 2006.
12. International Conference "Operator Theory, Analysis and Mathematical Physics", Lund, June 15-22, 2006.
11. International Conference "Semiclassical analysis and classical quantum mechanics", Bologna, March 9-11, 2006.
10. International Workshop "Spectra, Algorithms, and Data Analysis", Hradec Kralove, February 28 - March 1, 2006.
9. International Conference "Multi-scale problems: modelling, analysis and applications", Bath, September 12-14, 2005.
8. International Conference "Differential Equations and Related Topics" dedicated to Ivan G. Petrovskii, Moscow, May 16-22, 2004.
7. International workshop "Guided Quantum Particles", Prague, May 9-15, 2002.
6. International Seminar "Day on Diffraction-2002", St. Peterburg, June 5-8, 2002.
5. International Conference "Asymptotics and Differential Equations". Ufa, May 28-30, 2002.
4. International Conference "Differential Equations and Related Topics" dedicated to the Centenary Anniversary of Ivan G. Petrovskii, Moscow, May 22-27, 2001.
3. International Conference "Complex Analysis, Differential Equaitons and Related Topics", Ufa, June 28-30, 2000.
2. Second International conference "Exactly Solvable models of Mathematical Physics", Chelyabinsk, August 3-8, 1998.
1. International conference "Differential Equations and Related Topics",Moscow, January 20-24, 1998.