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. I. Borisov, R. R. Suleimanov, “On operator estimates for elliptic equations in multi-dimensional domains with strongly curved boundary”, Mat. Sb. (to appear)
2024
2.
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 (to appear) , arXiv: 2205.09490
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 (to appear)
5.
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
2023
6.
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, “Homogenization of Operators with Perturbations of General Form in the Lower-Order Terms”, Math. Notes, 113:1 (2023), 139–143
8.
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, 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, D. A. Zezyulin, “On bifurcations of thresholds in essential spectrum under presence of spectral singularity”, Differential Equations, 59:2 (2023), 278–282 https://doi.org/10.1134/S0012266123020118
11.
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, “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
13.
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, “On resolvent of the Schrödinger operator on a model graph with small loops”, Journal of Mathematical Sciences, 276:1 (2023), 48–60
16.
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.
17.
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.
18.
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.
19.
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, “Uniform convergence for problems with perforation alogn a given manifold and with a nonlinear Robin condition on the boundaries of cavities”, Algebra i Analiz, 35:4 (2023), 20–78
2022
21.
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, 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
23.
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
24.
D. I. Borisov, E. A. Zhizhina, A. L. Piatnitski, “Spectrum of a convolution operator with potential”, Russian Math. Surveys, 77:3 (2022), 546–548
25.
D. I. Borisov, A. A. Fedotov, “On Bloch solutions of difference equations”, Funct. Anal. Appl., 56:4 (2022), 239–250
26.
D. I. Borisov, “Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case”, Ufa Mathematical Journal, 14:4 (2022), 26–41
27.
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.
28.
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
29.
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
30.
D. I. Borisov,M. Znojil, “Arnold’s potentials and quantum catastrophes II”, Annals of Physics, 442 (2022), 168896 , 15 pp.
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, “Norm resolvent convergence of elliptic operators in domains with thin spikes”, Journal of Mathematical Sciences, 261:3 (2022), 366–391
2021
33.
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, 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. 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, P. Exner, “Gap opening in two-dimensional periodic systems”, Communications in Contemporary Mathematics, 23:1 (2021), 1950080 , arXiv: 1810.08824
37.
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
38.
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
39.
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
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
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
2020
45.
D.I. Borisov, D.A. Zezyulin, “Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials”, Applied Mathematics Letters, 100 (2020), id 106049 , arXiv: 1908.06384
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
47.
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.
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, 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, A. I. Mukhametrakhimova, “On a model graph with a loop and small edges”, Journal of Mathematical Sciences, 251:5 (2020), 573-601
51.
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
52.
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, “On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a strip with oscillating boundary”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 3–14
55.
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
56.
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
57.
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, “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
2020
60.
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
2018
61.
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
62.
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. 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, 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
2019
65.
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
2018
66.
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.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, “On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation”, Ufa Math. Journal, 10:2 (2018), 14–30
2021
69.
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
2017
70.
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. 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, M. Znojil, “On eigenvalues of a $\mathscr{P\!T}$-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199
2019
74.
D.I. Borisov, “Estimates of initial scales for layers with small random negative-definite perturbations”, Journal of Mathematical Sciences, 241:5 (2019), 518–548
2017
75.
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
76.
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
2016
77.
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, 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. 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. 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, 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, 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
85.
JETP Letters, 101:7 (2015), 497–502
86.
D.I. Borisov, “The Emergence of Eigenvalues of a $\mathcal{PT}$-Symmetric Operator in a Thin Strip”, Math. Notes, 98:6 (2015), 872–883
87.
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. 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
89.
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. 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. 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. 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. 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. 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
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
2013
99.
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
100.
D.I. Borisov, K. V. Pankrashin, “On the Extrema of Band Functions in Periodic Waveguides”, Funct. Anal. Appl., 47:3 (2013), 238–240
101.
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, 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, P. Exner, A. Golovina, “Tunneling resonances in systems without a classical trapping”, Journal of Mathematical Physics, 54:1 (2013), id–012102
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, P. Freitas, “On the spectrum of deformations of compact double-sided flat hypersurfaces”, Analysis & PDE, 6:5 (2013), 1051–1088 , Mathematical Sciences Publishers
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
108.
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, “On a $\mathcal{PT}$-symmetric waveguide with a pair of small holes”, Proc. Inst. Math. Mech., 281, suppl. 1 (2013), 5–21
2012
110.
D. I. Borisov, A. M. Golovina, “On the resolvents of periodic operators with distant perturbations”, Ufimsk. Mat. Zh., 4:2 (2012), 65–73
111.
D. Borisov, G. Cardone, “Planar waveguide with “twisted” boundary conditions: small width”, Journal of Mathematical Physics, 53:2 (2012), 023503 , AIP Publishing
D. Borisov, I. Veselic, “Spectral gaps for self-adjoint second order operators”, Zeitschrift für Analysis und ihre Anwendungen, 31:4 (2012), 473–505
114.
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, “On the spectrum of a two-dimensional periodic operator with a small localized perturbation”, Izv. Math., 75:3 (2011), 471–505
116.
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, 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. 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. 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"
121.
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.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
2010
123.
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, 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, 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. 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, I. Veselić, “Spectral properties of weak-disorder quantum waveguides”, Oberwolfach Reports, 6:4 (2009), 2980–2981
128.
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. I. Borisov, “Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients”, St. Petersburg Math. J., 20:2 (2009), 175–191
2008
130.
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
131.
D. Borisov, D. Krejčiřík, “PT-symmetric waveguide”, Integral Equations and Operator Theory, 62:4 (2008), 489–515
D. I. Borisov, R. R. Gadyl'shin, “Errata”, Mat. Sb., 199:3 (2008), 160
2007
133.
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
134.
D. I. Borisov, “Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S35–S45
135.
D. I. Borisov, “Some singular perturbations of periodic operators”, Theoret. and Math. Phys., 151:2 (2007), 614–624
136.
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, 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. Borisov, “On a quantum waveguide with a small PT-symmetric perturbation”, Acta Polytechnica, 47:2–3 (2007)
140.
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, “Discrete spectrum of an asymmetric pair of waveguides coupled through a window”, Sb. Math., 197:4 (2006), 475–504
142.
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
143.
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
144.
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, “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, “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
2005
147.
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
148.
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, “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
150.
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 and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions”, Izv. Math., 67:6 (2003), 1101–1148
152.
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
2002
153.
D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008
154.
D.I. Borisov, “On a Singularly Perturbed Boundary Value Problem for the Laplacian in a Cylinder”, Differ. Equ., 38:8 (2002), 1140–1148
155.
D. I. Borisov, “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady. Mathematics, 65, no. 2, Pleiades Publishing, 2002, 224–226
156.
D. Borisov, “Dvuparametricheskie asimptotiki sobstvennykh chisel Laplasiana s chastym cheredovaniem granichnykh uslovii”, Vestnik molodykh uchenykh, 2002:1 (2002), 36–52
157.
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. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Math. Notes, 70:4 (2001), 471–485
159.
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, “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, R. R. Gadyl'shin, “On the spectrum of the Laplacian with frequently alternating boundary conditions”, Theoret. and Math. Phys., 118:3 (1999), 272–277
1998
162.
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
2024
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