Gadyl'shin Rustem Rashitovich

Publications in Math-Net.Ru

1. On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type
   
   Izv. RAN. Ser. Mat., 82:6 (2018),  37–64
2. On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case
   
   Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  56–70
3. On asymptotic formula for electric resistance of conductor with small contacts
   
   Ufimsk. Mat. Zh., 7:3 (2015),  16–28
4. On Friedrichs inequalities for a disk
   
   Trudy Inst. Mat. i Mekh. UrO RAN, 18:2 (2012),  48–61
5. Perturbation of a periodic operator by a narrow potential
   
   TMF, 173:1 (2012),  127–134
6. Perturbation of an elliptic operator by a narrow potential in an $n$-dimensional domain
   
   Ufimsk. Mat. Zh., 4:2 (2012),  28–64
7. Perturbation of the Shrödinger operator by a narrow potential
   
   Ufimsk. Mat. Zh., 3:3 (2011),  55–66
8. On the asymptotics of a solution of a boundary value problem in a domain perforated along boundary
   
   Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14,  27–36
9. Schrödinger operator on the axis with potentials depending on two parameters
   
   Algebra i Analiz, 22:6 (2010),  50–66
10. On the spectrum of a periodic operator with a small localized perturbation
    
    Izv. RAN. Ser. Mat., 72:4 (2008),  37–66
11. The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis
    
    Mat. Sb., 198:8 (2007),  3–34
12. On the spectrum of the Schrödinger operator with large potential concentrated on a small set
    
    Mat. Zametki, 79:5 (2006),  787–790
13. The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential
    
    TMF, 147:1 (2006),  58–63
14. Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006),  102–115
15. On the eigenvalues of a “dumb-bell with a thin handle”
    
    Izv. RAN. Ser. Mat., 69:2 (2005),  45–110
16. Local Perturbations of Quantum Waveguides
    
    TMF, 145:3 (2005),  358–371
17. Local Perturbations of the Schrödinger Operator on the Plane
    
    TMF, 138:1 (2004),  41–54
18. Scattering by a Cylindrical Trap in the Critical Case
    
    Mat. Zametki, 73:3 (2003),  355–370
19. On domains with a narrow isthmus in the critical case
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003),  50–55
20. Perturbation of soliton for Davey–Stewartson II equation
    
    Mat. Fiz. Anal. Geom., 9:2 (2002),  272–280
21. Analogues of the Helmholtz resonator in homogenization theory
    
    Mat. Sb., 193:11 (2002),  43–70
22. On a Model Analogue of the Helmholtz Resonator in Homogenization
    
    Trudy Mat. Inst. Steklova, 236 (2002),  79–86
23. Local Perturbations of the Schrödinger Operator on the Axis
    
    TMF, 132:1 (2002),  97–104
24. Homogenization and asymptotics for a membrane with closely spaced clamping points
    
    Zh. Vychisl. Mat. Mat. Fiz., 41:12 (2001),  1857–1869
25. Resonator systems
    
    Izv. RAN. Ser. Mat., 64:3 (2000),  51–96
26. On the Dirichlet problem for the Helmholtz equation on the plane with boundary conditions on an almost closed curve
    
    Mat. Sb., 191:6 (2000),  43–68
27. Asymptotics of the eigenvalues of a boundary value problem with rapidly oscillating boundary conditions
    
    Differ. Uravn., 35:4 (1999),  540–551
28. A boundary value problem for the Laplacian with rapidly changing type of boundary conditions in a multi-dimensional domain
    
    Sibirsk. Mat. Zh., 40:2 (1999),  271–287
29. Structural instability of a soliton for the Davey–Stewartson II equation
    
    TMF, 118:3 (1999),  354–361
30. On the spectrum of the Laplacian with frequently alternating boundary conditions
    
    TMF, 118:3 (1999),  347–353
31. On the asymptotics of eigenvalues for a periodically fixed membrane
    
    Algebra i Analiz, 10:1 (1998),  3–19
32. Asymptotic behaviour of the eigenvalues of the Dirichlet problem in a domain with a narrow slit
    
    Mat. Sb., 189:4 (1998),  25–48
33. Characteristic frequencies of bodies with thin spikes. III. Frequency splitting
    
    Mat. Zametki, 61:4 (1997),  494–502
34. Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator
    
    Uspekhi Mat. Nauk, 52:1(313) (1997),  3–76
35. On scattering by a cylindrical surface with a narrow crack
    
    Differ. Uravn., 32:10 (1996),  1362–1370
36. On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey–Stewartson equation II
    
    TMF, 106:2 (1996),  200–208
37. On scattering by cylinder with narrow slit and with shell of finite depth
    
    TMF, 106:1 (1996),  24–43
38. On the perturbation of the Laplacian spectrum when the boundary condition type changes on a small part of the boundary
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:7 (1996),  77–88
39. Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:1 (1996),  92–102
40. A Complete Electromagnetic Analog of the Helmholtz Resonator
    
    Funktsional. Anal. i Prilozhen., 29:4 (1995),  1–16
41. On the existence of poles with a small imaginary part for a complete electromagnetic analogue of the Helmholtz resonator
    
    Dokl. Akad. Nauk, 338:2 (1994),  151–153
42. A two-dimensional analogue of the Helmholtz resonator with ideally rigid walls
    
    Differ. Uravn., 30:2 (1994),  221–229
43. On eigenfrequencies of bodies with thin branches. II. Asymptotics
    
    Mat. Zametki, 55:1 (1994),  20–34
44. On scattering by bodies with narrow channels
    
    Mat. Sb., 185:7 (1994),  39–62
45. On scattering of $H$-polarized electromagnetic field by ideal conductive cylinder with narrow lengthwise split of finite depth
    
    Zap. Nauchn. Sem. POMI, 210 (1994),  65–72
46. On the Poles of an Acoustic Resonator
    
    Funktsional. Anal. i Prilozhen., 27:4 (1993),  3–16
47. Splitting of the poles of a Helmholtz resonator
    
    Izv. RAN. Ser. Mat., 57:5 (1993),  44–74
48. Characteristic frequencies of bodies with thin spikes. I. Convergence and estimates
    
    Mat. Zametki, 54:6 (1993),  10–21
49. Splitting a multiple eigenvalue in the boundary value problem for a membrane clamped on a small part of the boundary
    
    Sibirsk. Mat. Zh., 34:3 (1993),  43–61
50. Asymptotic behavior of the second eigenfrequency for a system of two bodies connected by a thin rod
    
    TMF, 97:1 (1993),  68–77
51. Surface potentials and the method of matching asymptotic expansions in the Helmholtz resonator problem
    
    Algebra i Analiz, 4:2 (1992),  88–115
52. On a system of embedded resonators
    
    Dokl. Akad. Nauk, 326:6 (1992),  939–942
53. On merging poles of an acoustic resonator
    
    Dokl. Akad. Nauk, 324:4 (1992),  773–776
54. Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition
    
    Mat. Zametki, 52:4 (1992),  42–55
55. Influence of the position of the opening and its shape on the properties of a Helmholtz resonator
    
    TMF, 93:1 (1992),  107–118
56. The Helmholtz resonator with a small aperture
    
    Zh. Vychisl. Mat. Mat. Fiz., 32:9 (1992),  1464–1475
57. The amplitude of oscillations for a Helmholtz resonator
    
    Dokl. Akad. Nauk SSSR, 310:5 (1990),  1094–1097
58. Asymptotics of the eigenvalue of a singularly perturbed selfadjoint elliptic problem with a small parameter in the boundary conditions
    
    Differ. Uravn., 22:4 (1986),  640–652


59. Errata
    
    Mat. Sb., 199:3 (2008),  160
60. Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)
    
    Differ. Uravn., 38:8 (2002),  1011–1016