Borisov, Denis Ivanovich

Total publications: 125 (124)
in MathSciNet: 93 (92)
in zbMATH: 52 (52)
in Web of Science: 85 (85)
in Scopus: 120 (120)
Cited articles: 94
Citations in Math-Net.Ru: 249
Citations in Web of Science: 820
Citations in Scopus: 897
Presentations: 1

Number of views:
This page:4246
Abstract pages:9642
Full texts:3429
Borisov, Denis Ivanovich
Doctor of physico-mathematical sciences (2008)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 18.07.1978
Keywords: small parameter, perturbation, asymptotics, homogenization, spectrum, non-self-adjoint operator, band spectrum, eigenvalue.
UDC: 517.956, 517.956.226, 517.956.8, 517.958:621.372.8, 517.958:531.34, 517.958, 517.984, 519.63
MSC: 35J05, 35J10, 34E05, 34E10, 34E13, 34E15, 47F05, 47N50, 35P20


homogenization theory, spectral theory, asymptotic analysis.

Main publications:
  • 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.
List of publications on Google Scholar
List of publications on ZentralBlatt

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. D.I. Borisov, P. Exner, “Gap opening in two-dimensional periodic systems”, Communications in Contemporary Mathematics (to appear) , arXiv: 1810.08824  crossref  adsnasa  scopus
2. D. I. Borisov, A. I. Mukhametrakhimova, “Ravnomernaya skhodimost i asimptotiki dlya zadach v oblastyakh s melkoi perforatsiei vdol zadannogo mnogoobraziya v sluchae usrednennogo usloviya Dirikhle”, Matematicheskii sbornik (to appear)
3. 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 (to appear) , arXiv: 2003.03562
4. 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 (to appear)
5. D. I. Borisov, D. A. Zezyluin, M. Znojil, “Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations”, Studies in Applied Mathematics (to appear)
6. D. I. Borisov, P. Exner, “Approximation of point interactions by geometric perturbations in two-dimensional domains”, Proceedings of the London Mathematical Society (to appear)
7. D. I. Borisov, A. M. Golovina, “On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders”, Journal of Mathematical Analysis and Applications (to appear)
8. D. I. Borisov, A. I. Mukhametrakhimova, “Uniform convergence and asymptotics for problems in domains finely perforated along a given manifold in case of homogenized Dirichlet condition”, Mat. Sb. (to appear)  mathnet

9. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
10. D.I. Borisov, A.M. Golovina, A.I. Mukhametrakhimova, “Analiticheskoe prodolzhenie rezolventy ellipticheskogo operatora v mnogomernom tsilindre”, Problemy matematicheskogo analiza, 2020 (to appear)
11. 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.  crossref  isi (cited: 1)  scopus (cited: 1)
12. D. I. Borisov, O. A. Sultanov., “Asymptotic analysis of exit time for dynamical systems with a single well potential”, Journal of Differential Equations, 269:8 (2020), 78-116 , arXiv: 1906.04715  crossref  mathscinet  adsnasa  isi (cited: 1)  scopus (cited: 1)
13. 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.  crossref  isi (cited: 1)  scopus (cited: 1)
14. 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.  crossref  isi  scopus
15. D. I. Borisov, A. I. Mukhametrakhimova., “O modelnom grafe s petlei i malymi rebrami”, Problemy matematicheskogo analiza, 2020 (to appear)
16. D.I. Borisov, M.N. Konyrkulzhaeva, “O beskonechnoi sisteme rezonansov i sobstvennykh znachenii s eksponentsialnymi asimptotikami, porozhdennykh razbegayuschimisya vozmuscheniyami”, Ufimskii matematicheskii zhurnal, 12:4 (2020) (to appear)

17. 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  mathnet  mathscinet
18. 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  mathnet  crossref  mathscinet  isi  scopus (cited: 2)  scopus (cited: 2)
19. 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  crossref  mathscinet  zmath  scopus (cited: 1)
20. 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  crossref  isi (cited: 1)  scopus (cited: 2)
21. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
22. 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  mathnet  mathscinet  zmath

23. 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  crossref  mathscinet  scopus

24. 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  mathnet  crossref  crossref  adsnasa  isi (cited: 1)  elib  elib  scopus (cited: 3)  scopus (cited: 3)
25. 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  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
26. 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  crossref  mathscinet  isi (cited: 5)  scopus (cited: 6)
27. 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  crossref  mathscinet  zmath  zmath  scopus (cited: 4)

28. 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  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 1)  scopus (cited: 1)

29. M. Znojil, D. Borisov, “Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation”, Annals of Physics, 394 (2018), 40-49  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 6)
30. 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  crossref  mathscinet  zmath  isi  scopus (cited: 6)
31. 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  mathnet  crossref  isi (cited: 1)  scopus (cited: 2)  scopus (cited: 2)
32. D. I. Borisov, “Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf”, Mathematical physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 13–24  mathnet  mathscinet

33. 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  crossref  isi (cited: 3)  scopus (cited: 3)
34. 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  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 7)
35. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
36. D. I. Borisov, M. Znojil, “On eigenvalues of a $\mathscr{PT}$-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 3)  elib  elib  scopus  scopus

37. D.I. Borisov, “Estimates of initial scales for layers with small random negative-definite perturbations”, Journal of Mathematical Sciences, 241:5 (2019), 518–548  mathnet  crossref  mathscinet  zmath  scopus

38. 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
39. 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  mathnet  crossref

40. 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  crossref  mathscinet  zmath  isi (cited: 15)  scopus (cited: 18)
41. Math. Notes, 99:5 (2016), 636–642  mathnet  crossref  mathscinet  isi (cited: 3)  elib  elib  scopus (cited: 3)  scopus (cited: 3)
42. 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  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1)
43. 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  crossref  mathscinet  isi (cited: 1)  scopus (cited: 2)
44. 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  crossref  mathscinet  scopus; 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
45. 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  crossref  zmath  isi (cited: 11)  scopus (cited: 8)
46. 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  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 2)

47. 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  mathnet  crossref  mathscinet  isi (cited: 4)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 4)  scopus (cited: 4)
48. JETP Letters, 101:7 (2015), 497–502  mathnet  crossref  crossref  isi (cited: 10)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 9)  scopus (cited: 9)
49. D.I. Borisov, “The Emergence of Eigenvalues of a $\mathcal{PT}$-Symmetric Operator in a Thin Strip”, Math. Notes, 98:6 (2015), 872–883  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  elib  scopus (cited: 1)  scopus (cited: 1)
50. 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  crossref  mathscinet  isi (cited: 6)  scopus (cited: 7)
51. 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  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
52. 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  crossref  mathscinet  isi (cited: 13)  scopus (cited: 14)
53. 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  crossref  mathscinet  scopus (cited: 1)
54. 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  crossref  mathscinet  isi (cited: 10)  scopus (cited: 12)
55. 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  crossref  mathscinet  scopus (cited: 1)

56. D.I. Borisov, “Discrete spectrum of thin $\mathcal{PT}$-symmetric waveguide”, Ufa Math. Journal, 6:1 (2014), 29–55  mathnet  crossref  mathscinet  isi  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 5)  scopus (cited: 5)
57. D. Borisov, “Eigenvalues collision for PT-symmetric waveguide”, Acta Polytechnica, 54:2 (2014), 93–100 , arXiv: 1401.6316  crossref  elib  scopus (cited: 17)
58. D. Borisov, M. Tautenhahn, I. Veselic, “Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators”, Mathematical Results in Quantum Mechanics, 2014, 89–99  crossref  mathscinet
59. 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  crossref  mathscinet  isi (cited: 6)  elib (cited: 1)  scopus (cited: 6)
60. 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  crossref  isi (cited: 19)  elib (cited: 7)  scopus (cited: 22)
61. 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  elib

62. 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  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 13)  elib (cited: 5)  elib (cited: 5)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 12)  scopus (cited: 12)
63. D.I. Borisov, K. V. Pankrashin, “On the Extrema of Band Functions in Periodic Waveguides”, Funct. Anal. Appl., 47:3 (2013), 238–240  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 5)  scopus (cited: 5)
64. 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  crossref  mathscinet  isi (cited: 23)  scopus (cited: 25)
65. 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  crossref  mathscinet  isi (cited: 18)  scopus (cited: 20)
66. D. Borisov, I. Veselić, “Low lying eigenvalues of randomly curved quantum waveguides”, Journal of Functional Analysis, 265:11 (2013), 2877–2909 , Academic Press  crossref  mathscinet  isi (cited: 7)  scopus (cited: 8)
67. D. Borisov, P. Exner, A. Golovina, “Tunneling resonances in systems without a classical trapping”, Journal of Mathematical Physics, 54:1 (2013), id–012102  crossref  mathscinet  isi (cited: 4)  scopus (cited: 7)
68. 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  crossref  mathscinet  isi (cited: 18)  scopus (cited: 20)
69. 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  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1)
70. 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  mathscinet  elib
71. 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  crossref  mathscinet  isi (cited: 3)  scopus (cited: 3)
72. 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  mathnet  crossref  mathscinet  isi (cited: 5)  elib  elib  scopus (cited: 4)  scopus (cited: 4)

73. D. I. Borisov, A. M. Golovina, “On the resolvents of periodic operators with distant perturbations”, Ufimsk. Mat. Zh., 4:2 (2012), 65–73  mathnet  mathscinet  elib
74. D. Borisov, G. Cardone, “Planar waveguide with “twisted” boundary conditions: small width”, Journal of Mathematical Physics, 53:2 (2012), 023503 , AIP Publishing  crossref  mathscinet  isi (cited: 19)  scopus (cited: 17)
75. D. I. Borisov, P. Freitas, “Eigenvalue asymptotics for almost flat compact hypersurfaces”, Doklady Mathematics, 85, no. 1, 2012, 18–22  crossref  mathscinet  zmath  elib  scopus
76. D. Borisov, I. Veselic, “Spectral gaps for self-adjoint second order operators”, Zeitschrift für Analysis und ihre Anwendungen, 31:4 (2012), 473–505  crossref  mathscinet  zmath  isi  scopus
77. 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  crossref  mathscinet  isi (cited: 17)  scopus (cited: 18)

78. D. I. Borisov, “On the spectrum of a two-dimensional periodic operator with a small localized perturbation”, Izv. Math., 75:3 (2011), 471–505  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 10)  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 7)  scopus (cited: 7)
79. 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  crossref  mathscinet  isi (cited: 18)  elib (cited: 11)  scopus (cited: 17)
80. 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  crossref  mathscinet  scopus (cited: 17)
81. D. Borisov, I. Veselić, “Low lying spectrum of weak-disorder quantum waveguides”, Journal of Statistical Physics, 142:1 (2011), 58–77 , Springer US  crossref  mathscinet  isi (cited: 6)  scopus (cited: 8)
82. 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  crossref  mathscinet  isi (cited: 18)  scopus (cited: 17)
83. 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"  mathscinet  elib
84. 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  crossref  mathscinet  zmath  isi (cited: 17)  scopus (cited: 16)
85. 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  mathnet

86. 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  crossref  mathscinet  zmath  isi (cited: 30)  scopus (cited: 27)
87. 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  crossref  mathscinet  zmath  isi (cited: 28)  elib  scopus (cited: 31)

88. 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  crossref  mathscinet  isi (cited: 15)  scopus (cited: 14)
89. 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  crossref  mathscinet  zmath  isi (cited: 24)  scopus (cited: 26)
90. D. Borisov, I. Veselić, “Spectral properties of weak-disorder quantum waveguides”, Oberwolfach Reports, 6:4 (2009), 2980–2981  crossref
91. 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  crossref  mathscinet  zmath  isi (cited: 31)  scopus (cited: 32)
92. D. I. Borisov, “Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients”, St. Petersburg Math. J., 20:2 (2009), 175–191  mathnet  crossref  mathscinet  zmath  isi (cited: 16)  elib  elib  scopus (cited: 9)

93. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 19)  elib (cited: 9)  elib (cited: 9)  elib (cited: 9)  elib (cited: 9)  scopus (cited: 15)  scopus (cited: 15)
94. D. Borisov, D. Krejčiřík, “PT-symmetric waveguide”, Integral Equations and Operator Theory, 62:4 (2008), 489–515  crossref  mathscinet  zmath  isi (cited: 40)  scopus (cited: 41)

95. 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  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  elib (cited: 2)  elib (cited: 2)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 3)  scopus (cited: 3)
96. D. I. Borisov, “Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S35–S45  mathnet  crossref  elib  elib  scopus  scopus
97. D. I. Borisov, “Some singular perturbations of periodic operators”, Theoret. and Math. Phys., 151:2 (2007), 614–624  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib  elib  scopus (cited: 7)  scopus (cited: 7)
98. 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  crossref  mathscinet  isi (cited: 9)  scopus (cited: 11)
99. D. I. Borisov, “Distant perturbations of the Laplacian in a multi-dimensional space”, Annales Henri Poincare, 8, no. 7, 2007, 1371–1399  crossref  mathscinet  zmath  isi (cited: 9)  elib (cited: 9)  scopus (cited: 10)
100. 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  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  scopus (cited: 2)
101. D. Borisov, “On a quantum waveguide with a small PT-symmetric perturbation”, Acta Polytechnica, 47:2–3 (2007)  zmath
102. D. Borisov, “Asymptotic behaviour of the spectrum of a waveguide with distant perturbation”, Mathematical Physics, Analysis and Geometry, 10:2 (2007), 155–196  crossref  mathscinet  zmath  isi (cited: 11)  scopus (cited: 11)

103. D. I. Borisov, “Discrete spectrum of an asymmetric pair of waveguides coupled through a window”, Sb. Math., 197:4 (2006), 475–504  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 30)  elib (cited: 22)  elib (cited: 22)  elib (cited: 22)  elib (cited: 22)  scopus (cited: 21)  scopus (cited: 21)
104. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 9)  elib  elib  scopus (cited: 10)  scopus (cited: 10)
105. 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  mathnet  crossref  mathscinet  zmath  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 3)  scopus (cited: 3)
106. 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  crossref  mathscinet  isi (cited: 9)  scopus (cited: 8)
107. 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  crossref  mathscinet  scopus (cited: 7)
108. 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  crossref  mathscinet  zmath  isi  elib  scopus

109. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
110. 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  crossref  mathscinet  zmath  isi (cited: 16)  elib  scopus (cited: 15)

111. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 7)
112. 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  crossref  mathscinet  zmath  isi (cited: 27)  scopus (cited: 28)

113. 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  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 14)  elib (cited: 10)  elib (cited: 10)  scopus (cited: 12)  scopus (cited: 12)
114. 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  mathscinet  zmath  isi (cited: 16)  scopus (cited: 21)

115. D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 10)  elib (cited: 14)  elib (cited: 14)  scopus (cited: 8)  scopus (cited: 8)
116. D.I. Borisov, “On a Singularly Perturbed Boundary Value Problem for the Laplacian in a Cylinder”, Differ. Equ., 38:8 (2002), 1140–1148  mathnet  crossref  mathscinet  isi (cited: 4)  scopus (cited: 6)
117. D. I. Borisov, “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady. Mathematics, 65, no. 2, Pleiades Publishing, 2002, 224–226  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
118. D. Borisov, “Dvuparametricheskie asimptotiki sobstvennykh chisel Laplasiana s chastym cheredovaniem granichnykh uslovii”, Vestnik molodykh uchenykh, 2002:1 (2002), 36–52
119. 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  crossref  mathscinet  zmath  isi (cited: 30)  scopus (cited: 35)

120. D. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Math. Notes, 70:4 (2001), 471–485  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 6)  elib (cited: 6)
121. 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  crossref  mathscinet  zmath  isi (cited: 41)  scopus (cited: 43)
122. 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  crossref  isi (cited: 9)  scopus (cited: 11)

123. 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  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 15)  elib (cited: 14)  elib (cited: 14)  scopus (cited: 13)

124. 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

Presentations in Math-Net.Ru
1. Асимптотический анализ в задачах математической физики
D.I. Borisov
Conference of Professors of the RAS in the Department of Mathematical Sciences of the Russian Academy of Sciences
June 15, 2016 10:00   

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