D. I. Borisov. Asimptotiki i otsenki sobstvennykh elementov Laplasiana s chastoi neperiodicheskoi smenoi granichnykh uslovii // Izvestiya RAN. Seriya matematicheskaya. 2003. T. 67. No. 6. C. 23-70
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.
D.I. Borisov. O spektre dvumernogo periodicheskogo operatora s malym lokalizovannym vozmuscheniem // Izvestiya RAN. Seriya matematicheskaya. 2011. T. 75. # 3. S. 29-64.
D.I. Borisov, K.V. Pankrashkin. Otkrytie lakun i rasscheplenie kraev zon dlya volnovodov, soedinennykh periodicheskoi sistemoi malykh okon // Matematicheskie zametki. 2013. T. 93, # 5. S. 665-683.
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.
D. Borisov, P. Exner, R. Gadyl'shin, “Geometric coupling thresholds in a two-dimensional strip”, Journal of Mathematical Physics, 43:12 (2002), 6265-6278 , arXiv: quant-ph/0206113
D. Borisov, P. Exner, R. Gadyl'shin, D. Krejčiřík, “Bound states in weakly deformed strips and layers”, Annales Henri Poincare, 2:3 (2001), 553-572 , arXiv: math-ph/0011052
D. I. Borisov, “Discrete spectrum of an asymmetric pair of waveguides coupled through a window”, Sb. Math., 197:4 (2006), 475–504
4.
D. Borisov, G. Cardone, L. Faella, C. Perugia, “Uniform resolvent convergence for strip with fast oscillating boundary”, Journal of Differential Equations, 255:12 (2013), 4378–4402 , Academic Press
D. Borisov, G. Cardone, T. Durante, “Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve”, Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 146:6 (2016), 1115–1158 , arXiv: 1305.1009
D. Borisov, R. Bunoiu, G. Cardone, “Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics”, Zeitschrift für angewandte Mathematik und Physik, 64:3 (2013), 439–472 , SP Birkhäuser Verlag Basel
D. Borisov, R. Bunoiu, G. Cardone, “On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition”, Annales Henri Poincare, 11:8 (2010), 1591–1627 , arXiv: 1010.2072
D. Borisov, G. Cardone, “Homogenization of the planar waveguide with frequently alternating boundary conditions”, Journal of Physics A: Mathematics and General, 42:36 (2009), 365205 , 21 pp., arXiv: 0905.0338
D. Borisov, P. Freitas, “Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in $R^d$”, Journal of Functional Analysis, 258:3 (2010), 893–912
D. Borisov, P. Freitas, “Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions on thin planar domains”, Annales de l'Institut Henri Poincare (C) Analyse non-lineaire, 26:2 (2009), 547–560 , arXiv: 0712.3245
D. Borisov, P. Exner, “Exponential splitting of bound states in a waveguide with a pair of distant windows”, Journal of Physics A: Mathematics and General, 37:10 (2004), 3411–3428
D. I. Borisov, “Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients”, St. Petersburg Math. J., 20:2 (2009), 175–191
14.
D. I. Borisov, R. R. Gadyl'shin, “On the spectrum of a periodic operator with a small localized perturbation”, Izv. Math., 72:4 (2008), 659–688
15.
D. I. Borisov, “Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions”, Izv. Math., 67:6 (2003), 1101–1148
16.
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, 176:6 (2011), 774–785 , Springer US
D. I. Borisov, K. V. Pankrashin, “Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows”, Math. Notes, 93:5 (2013), 660–675
19.
D. I. Borisov, R. R. Gadyl'shin, “On the spectrum of the Laplacian with frequently alternating boundary conditions”, Theoret. and Math. Phys., 118:3 (1999), 272–277
20.
D. I. Borisov, F. Ružička, M. Znojil, “Multiply degenerate exceptional points and quantum phase transitions”, International Journal of Theoretical Physics, 54:12 (2015), 4293–4305 , Springer US
D. Borisov, K. Pankrashkin, “Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones”, Journal of Physics A: Mathematical and Theoretical, 46:23 (2013), 235203 , IOP Publishing
D. Borisov, T. Ekholm, H. Kovařík, “Spectrum of the magnetic Schrodinger operator in a waveguide with combined boundary conditions”, Annales Henri Poincare, 6:2 (2005), 327–342 , arXiv: math-ph/0405034
D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008
25.
D. Borisov, R. Bunoiu, G. Cardone, “On a waveguide with an infinite number of small windows”, Comptes Rendus Mathematique, 349:1 (2011), 53–56 , Elsevier
D. Borisov, P. Freitas, “Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation”, Journal of Differential Equations, 247:11 (2009), 3028–3039 , Elsevier
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, no. 3, 283-298
28.
D. I. Borisov, “On the spectrum of a two-dimensional periodic operator with a small localized perturbation”, Izv. Math., 75:3 (2011), 471–505
29.
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”, Sb. Math., 212:8 (2021), 1068–1121
30.
D. I. Borisov, “Distant perturbations of the Laplacian in a multi-dimensional space”, Annales Henri Poincare, 8, no. 7, 2007, 1371–1399
D. I. Borisov, R. R. Gadyl'shin, “The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential”, Theoret. and Math. Phys., 147:1 (2006), 496–500
32.
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 $\phi$ 4 model”, Communications in Nonlinear Science and Numerical Simulation, 29:1 (2015), 267–282 , Elsevier
D. Saadatmand, S. V. Dmitriev, D. I. Borisov, P. G. Kevrekidis, “Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect”, Physical Review E, 90:5 (2014), 052902 , American Physical Society
D. Borisov, “Asymptotic behaviour of the spectrum of a waveguide with distant perturbation”, Mathematical Physics, Analysis and Geometry, 10:2 (2007), 155–196
D. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Math. Notes, 70:4 (2001), 471–485
36.
D. I. Borisov, T. F. Sharapov, “On the Resolvent of Multidimensional Operators with Frequently Alternating Boundary Conditions with the Robin Homogenized Condition”, Journal of Mathematical Sciences, 213:4 (2016), 461–503 , Springer US ; D. I. Borisov, T. F. Sharapov, “O rezolvente mnogomernykh operatorov s chastoi smenoi kraevykh uslovii v sluchae tretego usrednennogo usloviya”, Problemy matematicheskogo analiza, 83 (2015), 3-40
D. Borisov, G. Cardone, “Planar waveguide with “twisted” boundary conditions: Discrete spectrum”, Journal of Mathematical Physics, 52:12 (2011), 123513–123513 , American Institute of Physics
D. Borisov, G. Cardone, “Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional rods”, ESAIM: Control, Optimisation, and Calculus of Variation, 17:3 (2011), 887–908 , arXiv: 0910.3907
D. Borisov, P. Exner, “Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case”, Journal of Mathematical Physics, 47:11 (2006), 113502–1
D. I. Borisov, “Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions”, Journal of Mathematical Sciences, 264:5 (2022), 562–580
41.
D. Borisov, G. Cardone, “Planar waveguide with “twisted” boundary conditions: small width”, Journal of Mathematical Physics, 53:2 (2012), 023503 , AIP Publishing
D. Borisov, D. Krejčiřík, “The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions”, Asymptotic Analysis, 76:1 (2012), 45–59 , arXiv: 1102.5051
D. I. Borisov, “Some singular perturbations of periodic operators”, Theoret. and Math. Phys., 151:2 (2007), 614–624
44.
D. Borisov, “The spectrum of two quantum layers coupled by a window”, Journal of Physics A: Mathematical and Theoretical, 40:19 (2007), 5045 , IOP Publishing
D. I. Borisov, J. Kříž, “Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit”, Analysis and Mathematical Physics, 13 (2023), 5 , 34 pp.
D. I. Borisov, “On a $\mathcal{PT}$-symmetric waveguide with a pair of small holes”, Proc. Inst. Math. Mech., 281, suppl. 1 (2013), 5–21
47.
D. I. Borisov, “Asymptotics and estimates of the convergence rate in a three-dimensional boundary-value problem with rapidly alternating boundary conditions”, Siberian Math. J., 45:2 (2004), 222–240
48.
M. Znojil, D. Borisov, “Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation”, Annals of Physics, 394 (2018), 40-49
D. Borisov, P. Exner, A. Golovina, “Tunneling resonances in systems without a classical trapping”, Journal of Mathematical Physics, 54:1 (2013), id–012102
D. Saadatmand, D.I. Borisov, P.G. Kevrekidis, K. Zhou, S.V. Dmitriev, “Resonant interaction of φ4 kink with spatially periodic PT-symmetric perturbation with spatially periodic gain/loss coefficient”, Communications in Nonlinear Science and Numerical Simulation, 56 (2018), 62-76
D. I. Borisov, “On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows”, Russian Journal of Mathematical Physics, 22:2 (2015), 153–160 , Pleiades Publishing
D.I. Borisov, “On a Singularly Perturbed Boundary Value Problem for the Laplacian in a Cylinder”, Differ. Equ., 38:8 (2002), 1140–1148
55.
D. Borisov, “Resolvents of elliptic operators on quantum graphs with small edges: holomorphy and Taylor series”, Advances in Mathematics, 397 (2022), 108125 , 48 pp., arXiv: 2102.12958
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, 146:4 (2021), 834-880
M. Znojil, D. I. Borisov, “Anomalous mechanisms of the loss of observability in non-Hermitian quantum models”, Nuclear Physics B, 957 (2020), 115064 , 19 pp.
D. I. Borisov, D. M. Polyakov, “Resolvent convergence for differential-difference operators with small variable translations”, Mathematics, 11:20 (2023), 4260 , 34 pp.
D. I. Borisov, D. M. Polyakov, “Resolvent convergence for differential-difference operators with small variable translations”, Mathematics, 11:20 (2023), 4260 , 33 pp.
D. I. Borisov, A. A. Fedotov, “On Bloch solutions of difference equations”, Funct. Anal. Appl., 56:4 (2022), 239–250
64.
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, 60:1 (2021), 48
D. I. Borisov, M. N. Konyrkulzhaeva, “Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum”, Ufa Math. J., 11:2 (2019), 56–70
66.
D. I. Borisov, A. M. Golovina, “On the resolvents of periodic operators with distant perturbations”, Ufimsk. Mat. Zh., 4:2 (2012), 65–73
67.
D. I. Borisov, R. R. Gadyl'shin, “The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis”, Sb. Math., 198:8 (2007), 1063–1093
68.
D. I. Borisov, “On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential”, Journal of Mathematical Sciences, 139:1 (2006), 6243–6322 , Springer
D. I. Borisov, A. I. Mukhametrakhimova, “On a model graph with a loop and small edges”, Journal of Mathematical Sciences, 251:5 (2020), 573-601
70.
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, 239:3 (2019), 248-267
71.
D. I. Borisov, S. V. Dmitriev, “On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation”, Studies in Applied Mathematics, 138:3 (2017), 317-342 , arXiv: 1512.01103
D. Borisov, P. Freitas, “The spectrum of geodesic balls on spherically symmetric manifolds”, Communications in Analysis and Geometry, 25:3 (2017), 507-544 , arXiv: 1603.02399
D.I. Borisov, R. Kh. Karimov, T. F. Sharapov, “Initial length scale estimate for waveguides with some random singular potentials”, Ufa Math. Journal, 7:2 (2015), 33–54
74.
D. Borisov, G. Cardone, T. Durante, “Norm-resolvent convergence for elliptic operators in domain with perforation along curve”, Comptes Rendus Mathematique, 352:9 (2014), 679–683 , Elsevier Masson
D.I. Borisov, K. V. Pankrashin, “On the Extrema of Band Functions in Periodic Waveguides”, Funct. Anal. Appl., 47:3 (2013), 238–240
76.
D. I. Borisov, “On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets”, Comput. Math. Math. Phys., 46:2 (2006), 271–281
77.
D. I. Borisov, “Spectra of elliptic operators on quantum graphs with small edges”, Mathematics, 9:16 (2021), 1874 , 24 pp.
D. I. Borisov, G. Cardone, “On a one-dimensional quadratic operator pencil with a small periodic perturbation”, ESAIM: Control, Optimisation and Calculus of Variations, 26 (2020), 21 , 32 pp.
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, 52:44 (2019), id 445202 , arXiv: 1908.06383
D. I. Borisov, “Gaps in the spectrum of the Laplacian in a band with periodic delta interaction”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S16–S23
81.
D. Borisov, M. Tautenhahn, I. Veselic, “Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations”, Journal of Mathematical Physics, 58:12 (2017), id 121502 , arXiv: 1512.06347
D. Borisov, P. Freitas, “Asymptotics for the Expected Lifetime of Brownian Motion on Thin Domains in $R^n$”, Journal of Theoretical Probability, 26:1 (2013), 284–309 , Springer
D. I. Borisov, R. R. Suleimanov, “On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with rapidly oscillating boundary”, Math. Notes, 116:2 (2024), 182–199
86.
D. I. Borisov, “Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term”, Mathematical Methods in the Applied Sciences, 47:6 (2024), 4122–4164 , arXiv: 2205.09490
D. I. Borisov, A. L. Piatnitski, E. A. Zhizhina., “On spectra of convolution operators with potentials”, Journal of Mathematical Analysis and Applications, 517:1 (2023), 126568 , 27 pp.
D. I. Borisov, P. Exner, “Approximation of point interactions by geometric perturbations in two-dimensional domains”, Bulletin of Mathematical Sciences, 13:2 (2023), 2250003 , 30 pp.
D. I. Borisov, “Homogenization for operators with arbitrary perturbations of coefficients”, Journal of Differential Equations, 369 (2023), 41–93 , arXiv: abs/2205.09490
D. I. Borisov, D. A. Zezyulin, “Bifurcations of essential spectra generated by a small non-Hermitian small hole. II. Eigenvalues and resonances”, Russian Journal of Mathematical Physics, 29:3 (2022), 321–341
D. I. Borisov, A. A. Fedotov, “On the spectrum of a non-self-adjoint quasiperiodic operator”, Dokl. Math., 104:3 (2021), 326–331
92.
D. I. Borisov, D. A. Zezyulin, “Bifurcations of essential spectra generated by a small non-Hermitian hole. I. Meromorphic continuations”, Russian Journal of Mathematical Physics, 28:4 (2021), 416–433
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, 1008 (2020), 012068
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, 1008 (2020), 012073
D.I. Borisov, “Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip”, Theoret. and Math. Phys., 195:2 (2018), 690–703
96.
D. I. Borisov, “Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions”, Journal of Mathematical Sciences, 205:2 (2015), 141–181 , Springer US
D. I. Borisov, A. A. Fedotov, “Monodromization and a PT-symmetric nonself-adjoint quasi-periodic operator”, Russian Journal of Mathematical Physics, 30:3 (2023), 294–309
D. I. Borisov, A. I. Mukhametrakhimova, “Asymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities”, Sb. Math., 213:10 (2022), 1318–1371
99.
D. I. Borisov, E. A. Zhizhina, A. L. Piatnitski, “Spectrum of a convolution operator with potential”, Russian Math. Surveys, 77:3 (2022), 546–548
100.
D. I. Borisov, M. N. Konyrkulzhaeva, “Operator $L_2$-estimates for two-dimensional problems with frequent alternation of boundary conditions”, Journal of Mathematical Sciences, 267:3 (2022), 319–337
101.
D. I. Borisov,M. Znojil, “Arnold’s potentials and quantum catastrophes II”, Annals of Physics, 442 (2022), 168896 , 15 pp.
D. I. Borisov, “Norm resolvent convergence of elliptic operators in domains with thin spikes”, Journal of Mathematical Sciences, 261:3 (2022), 366–391
103.
D. I. Borisov, A. M. Golovina, “On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders”, Journal of Mathematical Analysis and Applications, 496:2 (2021), 124809 , arXiv: 2008.07289
D. I. Borisov, “Quantum graphs with small edges: holomorphy of resolvents”, Doklady Mathematics, 103:3 (2021), 113–117
105.
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, 257:5 (2021), 3–18
106.
D. I. Borisov, M. N. Konyrkulzhaeva, “On infinite system of resonance and eigenvalues with exponential asymptotics generated by distant perturbations”, Ufa Math. J., 12:4 (2020), 3–18
107.
D. Borisov, F. Hoecker-Escuti, I. Veselic, “Expansion of the spectrum in the weak disorder regime for random operators in continuum space”, Communications in Contemporary Mathematics, 20:1 (2018), id 1750008
D. I. Borisov, “On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation”, Ufa Math. Journal, 10:2 (2018), 14–30
109.
D. I. Borisov, “On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 373–391
110.
D. Borisov, F. Hoecker-Escuti, I. Veselić, “Expansion of the almost sure spectrum in the weak disorder regime”, Journal of Functional Analysis, 270:5 (2016), 1684–1718 , Academic Press
D. I. Borisov, “Creation of spectral bands for a periodic domain with small windows”, Russian Journal of Mathematical Physics, 23:1 (2016), 19–34 , Pleiades Publishing
D. Borisov, A. Golovina, I. Veselić, “Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate”, Annales Henri Poincare, 17:9 (2016), 2341-2377
D.I. Borisov, “The Emergence of Eigenvalues of a $\mathcal{PT}$-Symmetric Operator in a Thin Strip”, Math. Notes, 98:6 (2015), 872–883
114.
A. R. Bikmetov, D. I. Borisov, “Discrete Spectrum of the Schrodinger Operator Perturbed by a Narrowly Supported Potential”, Theoret. and Math. Phys., 145:3 (2005), 1691–1702
115.
D. I. Borisov, D. M. Polyakov, “Uniform spectral asymptotics for Schroedinger operator on segment with delta-interaction”, Russian Journal of Mathematical Physics, 31:2 (2024), 149–161
D. I. Borisov, D. M. Polyakov, “Asymptotics for eigenvalues of Schroedinger operator with small translation and Dirichlet condition”, Doklady Mathematics, 109:3 (2024), 227–231
117.
D. I. Borisov, D. M. Polyakov, “Uniform asymptotics for eigenvalues of model Schrödinger operator with small translation”, Ufa Math. J., 16:3 (2024), 1–20
118.
D. I. Borisov, D. A. Zezyulin, “On bifurcations of thresholds in essential spectrum under presence of spectral singularity”, Differential Equations, 59:2 (2023), 278–282https://doi.org/10.1134/S0012266123020118
119.
D. I. Borisov, A. I. Mukhametrakhimova, “Uniform convergence for problems with perforation alogn a given manifold and with a nonlinear Robin condition on the boundaries of cavities”, St. Petersburg Math. J., 35:4 (2024), 611–652
120.
D. I. Borisov, M. Täufer, I. Veseli{\c}, “Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum”, Journal of Statistical Physics, 182:1 (2021), 1
D. I. Borisov, O.A. Sultanov, “Complete asymptotics for solution of singularly perturbed dynamical systems with single well potential”, Mathematics, 8:6 (2020), 949 , 17 pp.
D. I. Borisov, M. Znojil, “Mathematical and Physical Meaning of the Crossings of Energy Levels in PT-Symmetric Systems”, Non-Hermitian Hamiltonians in Quantum Physics, Springer International Publishing, 2016, 201–217
D. Borisov, P. Freitas, “On the spectrum of deformations of compact double-sided flat hypersurfaces”, Analysis & PDE, 6:5 (2013), 1051–1088 , Mathematical Sciences Publishers
D. I. Borisov, R. R. Gadyl’shin, “The spectrum of a periodic operator with a small localized perturbation”, Doklady Mathematics, 75, no. 2, Pleiades Publishing, 2007, 255–259
D. I. Borisov, R. R. Suleimanov, “Operator estimates for elliptic equations in multidimensional domains with strongly curved boundaries”, Sb. Math., 216:1 (2025), 25–53
126.
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for Schrödinger operator perturbed by translation operator”, Izv. Math., 89:3 (2025), 442–460
127.
D. I. Borisov, “Geometric approximation of point interactions in three-dimensional domains”, Mathematics, 12:7 (2024), 1031 , 26 pp.
D.I. Borisov, R.R. Suleimanov, “Operator estimates for problems in domains with singular curved boundary: Dirichlet and Neumann conditions”, Doklady Mathematics, 109:1 (2024), 6–11
129.
D.I. Borisov, R.R. Suleimanov, “Operator estimates for problems in domains with singular curved boundary: Dirichlet and Neumann conditions”, Doklady Mathematics, 109:1 (2024), 6–11
130.
D. I. Borisov, “Homogenization of Operators with Perturbations of General Form in the Lower-Order Terms”, Math. Notes, 113:1 (2023), 139–143
131.
D. I. Borisov, “Geometric approximation of point interactions in two-dimensional domains for non-self-adjoint operators”, Mathematics, 11:4 (2023), 947 , 23 pp. https://doi.org/10.3390/math11040947
D. I. Borisov, L. I. Gazizova, “Taylor series for resolvents of operators on graphs with small edges”, Proceedings of Steklov Institute of Mathematics, 317:Suppl. 1 (2022), S37–S54
133.
D. I. Borisov, “Asymptotic analysis of boundary-value problems for the Laplace operator with frequently alternating type of boundary conditions”, Partial Differential Equations, CMFD, 67, no. 1, PFUR, M., 2021, 14–129
134.
D. I. Borisov, A. M. Golovina, A. I. Mukhametrakhimova, “Analytic continuation of resolvent of analytic continuation in cylinder”, Journal of Mathematical Sciences, 250:2 (2020), 260-284
135.
D. I. Borisov, “Bethe-Sommerfeld conjecture for periodic Schroedinger operators in strip”, Journal of Mathematical Analysis and Applications, 479:1 (2019), 260–282 , arXiv: 1806.09292
D. I. Borisov, A. M. Golovina, “On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with scattering perturbations”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 3–14
137.
D.I. Borisov, M. Täufer, I. Veselić, “Spectral localization for quantum Hamiltonians with weak random delta interaction”, Comptes Rendus Mathématique, 356:6 (2018), 686-691
D.I. Borisov, “Estimates of initial scales for layers with small random negative-definite perturbations”, Journal of Mathematical Sciences, 241:5 (2019), 518–548
139.
D. I. Borisov, “Perturbation of Threshold of Essential Spectrum for Waveguides with Windows. II: Asymptotics”, Journal of Mathematical Sciences, 210:5 (2015), 590–621 , Springer US
D. Borisov, M. Tautenhahn, I. Veselic, “Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators”, Mathematical Results in Quantum Mechanics, 2014, 89–99
D. I. Borisov, “The asymptotics for the eigenelements of the Laplacian in a cylinder with frequently alternating boundary conditions”, Comptes Rendus de l'Académie des Sciences-Series IIB-Mechanics, 329:10 (2001), 717–721 , Elsevier
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for nonlocal one–dimensional Schroedinger operator with Neumann condition and translation in free term”, Lobachevskii Journal of Mathematics (to appear)
144.
D. I. Borisov, A. L. Piatnitski, E. A. Zhizhina, “Non-local convolution type operators with potential: essential and infinite discrete spectrum”, Mathematical Methods in the Applied Sciences, 2025 (to appear)
145.
S. V. Dmitriev, D. Xiong, D. I. Borisov, M. G. Velarde, “The effect of nonlinearity on the efficiency of a thermal rectifier in the form of a junction of two chains”, The European Physical Journal Special Topics, 2025 (to appear)
146.
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, 31:1 (2024), 321–341
147.
D. I. Borisov, A. A. Fedotov., “On the point spectrum of a non-self-adjoint quasiperiodic operator”, Russian Journal of Mathematical Physics, 31:3 (2024), 389–406
148.
D. I. Borisov, “Operator estimates in two-dimensional problems with a frequent alternation in the case of small parts with the Dirichlet condition”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S33–S52
149.
D. I. Borisov, “On resolvent of the Schrödinger operator on a model graph with small loops”, Journal of Mathematical Sciences, 276:1 (2023), 48–60
150.
D. I. Borisov, D. A. Zezyulin, “Eigenvalues bifurcating from continuum in two-dimensional potentials generating non-Hermitian gauge fields”, Annals of Physics, 459 (2023), 169498 , 17 pp.
151.
G. Berkolaiko, D. I. Borisov, M. King, “Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge”, Analysis and Mathematical Physics, 13 (2023), 90 , 22 pp.
152.
D. I. Borisov, A. L. Piatnitski and E. A. Zhizhina, “Spectrum of one-dimensional potential perturbed by a small convolution operator: general structure”, Mathematics, 11:19 (2023), 4042 , 26 pp.
153.
D. I. Borisov, A. L. Piatnitski, E. A. Zhizhina, “Spectrum of one-dimensional potential perturbed by a small convolution operator: general structure”, Mathematics, 11:19 (2023), 4042 , 26 pp.
154.
D. I. Borisov, “Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case”, Ufa Mathematical Journal, 14:4 (2022), 26–41
155.
S. V. Dmitriev, D. I. Borisov, “Effective interatomic potential for modelling shock waves in carbon nanotube bundles”, AIP Conference Proceedings, 2533 (2022), 02005 , 5 pp.
156.
D. I. Borisov, P. Exner, “Gap opening in two-dimensional periodic systems”, Communications in Contemporary Mathematics, 23:1 (2021), 1950080 , arXiv: 1810.08824
157.
D. I. Borisov, “On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a strip with oscillating boundary”, J. Math. Sci. (N. Y.), 257:3 (2021), 273–285
158.
D.I. Borisov, “On elliptic operators with frequent alternation of boundary conditions along a given curve”, Journal of Mathematical Sciences, 244:3 (2020), 378-389
159.
D. I. Borisov, “Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf”, J. Math. Sci. (N. Y.), 252:2 (2021), 135–146
160.
D.I. Borisov, “Initial length scale estimate for the Schroedginer operator with a random fast oscillating potential in a multi-dimensional layer”, Vestnik Kazakhskogo natsionalnogo universiteta. Seriya matematika, mekhanika, informatika., 93:1 (2017), 21-31
161.
D. Borisov, I. Nakić, Ch. Rose, M. Tautenhahn, I. Veselić, “Multiscale unique continuation properties of eigenfunctions”, Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, Springer International Publishing, 2015, 107–118
162.
S. V. Suchkov, D. I. Borisov, A. A. Sukhorukov, Yu. S. Kivshar, others, “Signal manipulation with a PT-symmetric coupler embedded into an array of optical waveguides”, Pisma o materialakh, 4:4 (2014), 222–225
163.
R. G. Akhmetov, D. I. Borisov, R. R. Gadylshin, A. R. Danilin, L. A. Kalyakin, O. M. Kiselev, E. F. Lelikova, V. Yu. Novokshenov, B. I. Suleimanov, “Pamyati Arlena Mikhailovicha Ilina”, Ufimskii matematicheskii zhurnal, 5:3 (2013) , Uchrezhdenie Rossiiskoi akademii nauk Institut matematiki s vychislitelnym tsentrom Ufimskogo nauchnogo tsentra Rossiiskoi akademii nauk
164.
D. Borisov, I. Veselic, “Spectral gaps for self-adjoint second order operators”, Zeitschrift für Analysis und ihre Anwendungen, 31:4 (2012), 473–505
165.
D. I. Borisov, “Ob usrednenii operatora Shrëdingera v polose s bystro menyayuschimsya tipom kraevykh uslovii”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 27, 6–11 , Gosudarstvennoe obrazovatelnoe uchrezhdenie vysshego professionalnogo obrazovaniya" Chelyabinskii gosudarstvennyi universitet"
166.
D.I. Borisov, “On the homogenization of Schrodinger operator in a strip with frequent alternation of boundary conditions”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14, 6–11
167.
D. Borisov, I. Veselić, “Spectral properties of weak-disorder quantum waveguides”, Oberwolfach Reports, 6:4 (2009), 2980–2981
168.
D. I. Borisov, “Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S35–S45
169.
D. Borisov, “On a quantum waveguide with a small PT-symmetric perturbation”, Acta Polytechnica, 47:2–3 (2007)
170.
D. I. Borisov, “Asymptotics of the spectrum of the Schrödinger operator perturbed by a rapidly oscillating periodic potential”, Doklady Mathematics, 73, no. 1, Pleiades Publishing, 2006, 19–22
171.
D. I. Borisov, “On a model boundary value problem for Laplacian with frequently alternating type of boundary condition”, Asymptotic Analysis, 35:1 (2003), 1-26
172.
D. I. Borisov, “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady. Mathematics, 65, no. 2, Pleiades Publishing, 2002, 224–226
173.
D. Borisov, “Dvuparametricheskie asimptotiki sobstvennykh chisel Laplasiana s chastym cheredovaniem granichnykh uslovii”, Vestnik molodykh uchenykh, 2002:1 (2002), 36–52
174.
D. I. Borisov, R. R. Gadyl'shin, “On Laplacian with rapidly and quasiperiodically changing type of boundary conditions”, Russian Mathematical Survey, 53:4 (1998), 813 , Russian Academy of Sciences
175.
D. I. Borisov, R. R. Suleimanov, “On operator estimates for elliptic equations in two-dimensional domains with fast oscillating boundary and frequent alternation of boundary conditions”, Sb. Math., 216:8 (2025), 1037–1054
176.
D. I. Borisov, E. A. Zhizhina, A. L. Piatnitski, “On infinite discrete spectrum of convolution operators with potentials”, Funktsional. Anal. i Prilozhen.
177.
D. I. Borisov, R. R. Gadyl'shin, “Errata”, Mat. Sb., 199:3 (2008), 160
178.
D. I. Borisov, A. R. Danilin, V. Yu. Novokshenov, “Tribute to Arlen Mikhailovich Il'in”, Sb. Math., 216:8 (2025), 1019–1020
