Rustem R. Gadyl'shin's Publications

Publications

All the publications are available by request: gadylshin@yandex .ru
Some articles can be downloaded online.

Articles

[108] A.R. BikmetovР., R.R. Gadyl'shin,
Perturbation of a elliptic operator by a narrow potential in f n-dimentional domain
Ufimskii matematicheskii zhurnal, 4:2 (2012), 28-64
English transl. in Ufa mathematicali journal, 4:2 (2012),

[107] R.R. Gadyl'shin, I.Kh. Khusnullin:
Perturbation of a periodic operator by a narrow potential
Teor. Mat. Fiz., 173:1 (2012), 127-134.
English transl. in Theor. Math. Phys., 173:1 (2012), 1438-1444

[106] R.R. Gadyl'shin, E.A. Shishkina:
On Friedrichs inequalities for a disk
Trudy Instituta Matrmatiki i Mekhaniki UrO RAN. 18:2 (2012) 48-61.
English transl. in Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 18:2 (2012)

[105] R.R. Gadyl'shin, Yu.O Koroleva, G.A. Chechkin:
On the asymptotics of a solution of a boundary value problem in a domain perforated along the boundary
Vestnik Chelyabinskogo gosudarstvennogo Universiteta. Matematika. Mekhanika. Informatika, 14:27 (2011), 27-36 (in Russian).

[104] R.R. Gadyl'shin, I.Kh. Khusnullin:
Perturbation of the Shrodinger operator by a narrow potential
Ufimskii matematicheskii zhurnal, 3:3 (2011), 55-66
English transl. in Ufa mathematicali journal, 3:3 (2011), 54-64
(http://matem.anrb.ru/sites/default/files/files/vupe11/Gadyl%27shin.pdf)

[103] R.R. Gadyl'shin, I.Kh. Khusnullin:
Schrodinger operator on the exis with potentials depending on two parameters
Algebra i analiz, 22:6 (2010), 50-66
English transl. in St. Ptersburg Math. J., 22:6 (2010), 50-66

[102] R.R. Gadyl'shin, Yu.O Koroleva, G.A. Chechkin:
On the eigenvalue of the Laplacian in a domain perforated along the boundary
Dokl. Acad. Nauk, 432:1 (2010), 7-11
English transl. in Doklady Mathematics, 81:3 (2010), 337-341

[101] R.R. Gadyl'shin, A.M. Il'in:
On the spectrum of the Neumann problem for Lalplace equation in a domain with a narrow slit
Asymptotic Analysis, 67:3,4 (2010), 167-189

[100] R.R. Gadyl'shin, Yu.O Koroleva, G.A. Chechkin:
On the asymptotic behavior of a simple eigenvalue of a boundary value problem in a domain perforated along the boundary
Differ. Uravn., 47:6 (2011), 822-831
English transl. Differ. Equations, 47:6 (2011), 819-828

[99] Youcef Amirat, Gregory A. Chechkin, Rustem R. Gadyl’shin:
Spectral boundary homogenization in domains with oscillating boundaries
Nonlinear Analysis: Real World Applications, 11:6 (2010), 4492-4499

[98]. A. Bikmetov, R. Gadylshin:
On quantum waveguide with shrinking potential
Russian Journal of Mathematical Physics, 17:1 (2010), 19-25

[97] R.R. Gadylshin:
On regular and singular perturbations of eigenelements of Laplacian
Proceedings of the Tenth International Conference on Integral Methods in Science and Engineering, 1 (2009) P.135-148.

[96] Y. Amirat, G.A. Chechkin, R.R. Gadyl'shin:
Asymptotic aproximation of eigenelements of the Dirichlet problem for the Laplacian in Domain in a domain with shoots
Mathematical Methods in the Applied Scienses, 33 (2010), 811-830

[95] R.R. Gadyl'shin, Yu.O Koroleva, G.A. Chechkin:
On the convergence of solutions and eigenelements of a boundary value problem in a domain perforated along the boundary
Differ. Uravn., 46:5 (2010), 665-677
English transl. Differ. Equations, 46:5 (2010), 667-680

[94] Y. Amirat, G.A. Chechkin, R.R. Gadyl'shin:
Asymptotics of the Solution of a Dirichlet Spectral Problem in a Junction with Highly Oscillating Boundary
Comptes Rendus Mecanique. 336:9 (2008), 693-698.

[93] D.I. Borisov, R.R. Gadyl'shin.
On spectrum of periodic operator with a small localized perturbation
Izv. Ross. Akad. Nauk, Ser. Mat. 72:4 (2008), 37-66
English transl. in Izv. Math. 72:4 (2008), 659-688

[92] Y. Amirat, G.A. Chechkin, R.R. Gadyl'shin:
Asymptotics for Eigenelements of Laplacian in Domain with Oscillating Boundary. Multiple Eigenvalues.
Applicable Analysis, 86:7 (2007), 873-898.

[91] D.I. Borisov, R.R. Gadyl'shin:
On spectrum of self-adjoint differential operator on the axis with fast oscillating coefficients
Mat. Sb., 198:8 (2007), 3-34.
English transl. in Sbornik Math.

[90] D.I. Borisov, R.R. Gadyl'shin:
On a periodic operator with a small localized perturbation
Dokl. Acad. Nauk, 413:4 (2007), 439-443
English transl. in Doklady Mathematics. 75:2 (2007), 255-259.

[89] G.A. Chechkin, R.R. Gadyl'shin:
On boundary-value problems for the Laplacian in bounded domains with micro inhomogeneous structure of the boundaries
Acta Mathematica Sinica, 23:2 (2007), 237-248.

[88] D.I. Borisov, R.R. Gadyl'shin:
On spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential
Teor. Mat. Fiz., 141:1 (2006), 48-53
English transl. in Theor. Math. Phys. 147:1 (2006), 485-489

[87] A.R. Bikmetov, R.R. Gadyl'shin:
On spectrum of the Schroedinger operatoron with a large potential concentrated on a small set
Matem. zametki, 79:5 (2006), 787–790.
English transl. in Math. Notes. 79:5-6 (2006), 729-733.

[86] R.R. Gadyl'shin:
Local perturbations of quantum waveguiedes
Teor. Mat. Fiz., 145:3 (2005), 359-372
English transl. in Theor. Math. Phys. 145:3 (2005), 1678-1690
[http://dx.doi.org/10.1007/s11232-005-0190-y]

[85] R.R. Gadyl'shin:
On eqigenvalues of "damp-bell with a thin handle"
Izv. Ross. Akad. Nauk, Ser. Mat. 69:2 (2005), 45-110
English transl. in Izv. Math. 69:2 (2005), 265-329

[84] R.R. Gadyl'shin:
On regular and singular perturbations of acoustic and quantum waveguides
Comptes Rendus Mecanique. 332:8 (2004) 647-652
[arXiv:math-ph/0402039]

[83] Y. Amirat, G.A. Chechkin, R.R. Gadyl'shin:
Asymptotics of simple egenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary
Zh. Vychisl. Mat. Mat. Fiz. 46:1 (2006), 102-115
English transl. Comput. Math. Math. Phys. 46:1 (2006), 97-110
[Prepublication du Laboratoire de Mathematiques Appliquees ]

[82] G.A. Chechkin, R.R. Gadyl'shin:
On boundary-value problems for the Laplacian in bounded and in unbounded domains with perforated boundaries
Journal of Differential Equations , 216 (2005), 502-522

[81] R.R. Gadyl'shin:
On resonant scattering in two-dimensional problem of
homogonezation
Dokl. Acad. Nauk, 397:2 (2004), 74-77.
English transl. in Doklady Mathematics. 70:1 (2004), 639-643.

[80] R.R. Gadyl'shin:
Concordance method of asymptotic expansions in a singularly-perturbed boundary-value problem for the Laplace operator
Itogi Nauki i Tekhniki. Sovremennay Matematika i Prilozheniya, 5 (2003), 3-32
English transl. in J. Math. Sciences, 125:5 (2005), 579-609.

[79] R.R. Gadyl'shin:
On local perturbations of the Schroedinger operator on the plane
Teor. Mat. Fiz. 138:1 (2004), 41-54.
English transl. in Theor. Math. Phys. 138:1 (2002), 33-44.
[arXiv: math-ph/0208025]

[78] R.R. Gadyl'shin:
On resonance in a homogenization problem
Comptes Rendus Mecanique. 331:9 (2003), 595-600

[77] R.R. Gadyl'shin:
On domains with a narrow connecting channel in a critical case
Trudy Instituta Matrmatiki i Mekhaniki UrO RAN. 9:1 (2003).
English transl. in Proceedings of the Steklov Institute of Mathematics, Suppl. 1 (2003), S68-S74.

[76] R.R. Gadyl'shin:
Scattering by a cylindrical trap in the critical case
Matem. zametki. 73:3 (2003), 355-370.
English transl. in Math. Notes. 73:3 (2003), 328-341.
[arXiv: math-ph/0210008]

[75] D. Borisov, P. Exner, R. Gadyl'shin:
Geometric coupling thresholds in a two-dimensional strip
J. Math. Phys. 43 (2002), 6265-6278 [arXiv:quant-ph/0206113; mp_arc 02-268]

[74] R.R. Gadyl'shin:
Eigenvalues of the Neumann Problem in a Domain with a Thin Channel
Dokl. Acad. Nauk. 387:1 (2002), 26-30.
English transl. in Doklady Mathematics. 66:3 (2002), 436-439.

[73] R.R. Gadyl'shin, A.M. Il'in:
On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit
[arXiv: math-ph/0208039]

[72] R.R. Gadyl'shin:
On analogues of Helmholtz resonator in homogenization theory
Mat. Sb. 193:11 (2002), 43-70
English transl. in Sbornik Math. 193:11 (2002), 1611-1638

[71] R.R. Gadyl'shin:
Helmholtz resonator and its analogs (in Russian)
Bashkir State Pedagogical University Journal. Natural Sciences. 1 (2002), 16-31

[70] R.R. Gadyl'shin:
On local perturbations of Shroedinger operator in axis
Teor. Mat. Fiz. 132:1 (2002), 97-104
English transl. in Theor. Math. Phys. 132:1 (2002), 976-982
[arXiv: math-ph/0202015]

[69] R.R. Gadyl'shin:
On a model analogue of the Helmholtz resonator in homogenization
in Proceedings of the International Conference on Differential Equations and Dynamical Systems (Suzdal 2000); Trudy Matem. Inst. Steklova 236 (2002), 79-86
English transl. Proc. Steklov Inst. Math. 236 (2002), 70-77

[68] R.R. Gadyl'shin, O.M. Kiselev:
Perturbation of solution for Davey-Stewartson II equation
Matem. Fizika. Analiz. Geom. 9:2 (2002), 272-280

[67] R.R. Gadyl'shin:
The scattering of plane wave by trap in the critical case
Prikl. Mat. Mekh. 66:1 (2002), 52-61
English transl. J. Appl. Math. Mech. 66:1 (2002), 49-57

[66] D. Borisov, P. Exner, R. Gadyl'shin, D. Krejcirik:
Bound states in weakly deformed strips and layers
Ann. Henri Poincar§Ы 2:3 (2001), 553-572
[arXiv:math-ph/0011052; mp_arc 00-473]

[65] R.R. Gadyl'shin:
Homogenization and asymptotics for a membrane with closely spaced clamping points
Zh. Vychisl. Mat. Mat. Fiz. 41:12 (2001), 1857-1869
English transl. Comput. Math. Math. Phys. 41:12 (2001), 1765-1776

[64] A.M. Il'in, R.R. Gadyl'shin:
On validity level of regular perturbation theory for membrane with narrow crack
Dokl. Akad. Nauk, Ross. Akad. Nauk 380:2 (2001), 172-175
English transl. Doklady Math. 64:2 (2001), 270-273

[63] R.R. Gadyl'shin:
On the scattering of $H$-polarized electromagnetic field by an ideally conductive cylindrical body of a trapping type
C. R. Acad. Sci., Paris, Ser. II b 329:2 (2001), 137-140

[62] R.R. Gadyl'shin:
Eigenvalues and scattering frequencies for domain with narrow appendixes and tubes
C. R. Acad. Sci., Paris, Ser. II b 329:10 (2001), 723-726

[61] R.R. Gadyl'shin:
On an eigenvalue of the Dirichlet problem in locally pertubed cylinder (in Russian)
in "Collection scientific papers of department of physics and mathematics", Ufa 2001, pp. 38-47

[60] R.R. Gadyl'shin:
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
English transl. Sb. Math. 191:6 (2000), 821-848

[59] R.R. Gadyl'shin:
Resonator systems
Izv. Ross. Akad. Nauk, Ser. Mat. 64:3 (2000), 51-96
English transl. Izv. Math. 64, No.3 (2000), 487-529

[58] R.R. Gadyl'shin:
On scattering by trap with narrow connecting channel (in Russian)
in Proceedings of the International Conference on Complex Analysis, Differential Equations and related topics (Ufa 2000), Differential Equations, vol. 1, Ufa 2000; pp. 42-48

[57] D.I. Borisov, R.R. Gadyl'shin:
On the spectrum of the Laplacian with frequently alternating boundary conditions
in Proceedings of the International Conference on Exactly Solvable Models of Mathematical Physics (Chelyabinsk 1998); Teor. Mat. Fiz. 118:3 (1999), 347-353
English transl. Theor. Math. Phys. 118:3 (1999), 272-277

[56] R.R. Gadyl'shin, O.M. Kiselev:
Structural instability of a soliton for the Davey-Stewartson II equation
in Proceedings of the International Conference on Exactly Solvable Models of Mathematical Physics (Chelyabinsk 1998); Teor. Mat. Fiz. 118:3 (1999), 354-381
English transl. Theor. Math. Phys. 118:3 (1999), 278-284

[55] A.G. Belyaev, G.A. Chechkin, R.R. Gadyl'shin:
Effective membrane permeability: Estimates and low concentration asymptotics
SIAM J. Appl. Math. 60:1 (1999), 84-108

[54] R.R. Gadyl'shin, G.A. Chechkin:
A boundary value problem for the Laplacian with rapidly changing type of boundary conditions in a multidimensional domain
Sib. Mat. Zh. 40:2 (1999), 271-287
English transl. Sib. Math. J. 40:2 (1999), 229-244

[53] R.R. Gadyl'shin:
On an analog of the Helmholtz resonator in the averaging theory
C. R. Acad. Sci., Paris, Ser. I, Math. 329:12 (1999), 1121-1126

[52] R.R. Gadyl'shin:
Asymptotics of the eigenvalues of a boundary value problem with rapidly oscillating boundary conditions
Differ. Uravn. 35:4 (1999), 540-551
English transl. Differ. Equations 35:4 (1999), 540-551

[51] R.R. Gadyl'shin:
On the Laplacian with fast changing type of the boundary conditions (in Russian)
in "Mathematical methods in natural history", Ufa 1999; pp. 59-65

[50] R.R. Gadyl'shin:
A system of embedded resonators
Tr. St. Peterbg. Mat. Obshch. 5 (1998), 43-68
English transl. Transl., Ser. 2, Am. Math. Soc. 193 (1999) 27-44

[49] R.R. Gadyl'shin:
Boundary value problem for the Laplacian with rapidly oscillating boundary conditions
Dokl. Akad. Nauk, Ross. Akad. Nauk 362:4 (1998), 456-459
English transl. Dokl. Math. 58:2 (1998), 293-296

[48] R.R. Gadyl'shin, A.M. Il'in:
Asymptotic behaviour of the eigenvalues of the Dirichlet problem in a domain with a narrow slit
Mat. Sb. 189:4 (1998), 25-48
English transl. Sb. Math. 189:4 (1998), 503-526

[47] R.R. Gadyl'shin:
On the eigenvalue asymptotics for periodically clamped membranes
Algebra Anal. 10:1 (1998), 3-19
English transl. St. Petersbg. Math. J. 10:1 (1999), 1-14

[46] R.R. Gadyl'shin:
Characteristic frequencies of bodies with thin spikes. III: Frequency splitting
Mat. Zametki 61:4 (1997), 494-502
English transl. Math. Notes 61:4 (1997), 409-416

[45] R.R. Gadyl'shin:
Asymptotics of poles with small imaginary part for a complete electromagnetic analog of the Helmholtz resonator
Russ. J. Math. Phys. 5:3 (1997), 307-320

[44] R.R. Gadyl'shin:
Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator
Usp. Mat. Nauk 52:1 (1997), 3-76
English transl. Russ. Math. Surv. 52:1 (1997), 1-72

[43] R.R. Gadyl'shin:
Scattering on a cylindrical surface with a narrow gap
Differ. Uravn. 32:10 (1996), 1362-1370
English transl. Differ. Equations 32:10 (1996), 1358-1367

[42] R.R. Gadyl'shin:
On scattering by a cylinder with a narrow slit and walls of finite thickness
Teor. Mat. Fiz. 106:1 (1996), 24-43
English transl. Theor. Math. Phys. 106:1 (1996), 19-34

[41] R.R. Gadyl'shin R.R., O.M. Kiselev:
On the soliton-free structure of scattering data on perturbation of a two-dimensional soliton for the Davey-Stewartson equation II
Teor. Mat. Fiz. 106:2 (1996), 200-208
English transl. Theor. Math. Phys. 106:2 (1996), 167-173

[40] R.R. Gadyl'shin:
The asymptotics form of solutions of singularly perturbed Dirichlet problem
Zh. Vychisl. Mat. Mat. Fiz. 36:1 (1996), 92-102
English transl. Comput. Math. Math. Phys. 36:1 (1996), 75-84

[39] R.R. Gadyl'shin:
Perturbation of the Laplacian spectrum when there is a change in the type of boundary condition on small part of the boundary
Zh. Vychisl. Mat. Mat. Fiz. 36:7 (1996), 77-88
English transl. Comput. Math. Math. Phys. 36, No.7 (1996), 889-898

[38] R.R. Gadyl'shin:
Asymptotics of the minimum eigenvalue for a circle with fast oscillating boundary conditions
C. R. Acad. Sci., Paris, Ser. I 323:3 (1996), 319-323

[37] R.R. Gadyl'shin:
A complete electromagnetic analog of the Helmholtz resonator
Funkts. Anal. Prilozh. 29:4 (1995), 1-16
English transl. Funct. Anal. Appl. 29:4 (1995), 225-237

[36] R.R. Gadyl'shin:
Asymptotic of a pole with small imaginary part for complete electromagnetic analogue of Helmholtz resonator
C. R. Acad. Sci., Paris, Ser. I 320:9 (1995), 1103-1106

[35] R.R. Gadyl'shin:
On complete electromagnetic analogue of the Helmholtz resonator. Existence of poles with small imaginary parts
C. R. Acad. Sci., Paris, Ser. I 320:7 (1995), 803-807

[34] R.R. Gadyl'shin:
On scattering of polarized electromagnetic field by ideal conductive cylinder with narrow slit
in "Asymptotics and symmetries in nonlinear dynamical systems", Ufa 1995; pp. 105-119

[33] R.R. Gadyl'shin:
Systems of acoustic resonators in the quasistationary mode
Prikl. Mat. Mekh. 58:3 (1994), 104-112
English transl. J. Appl. Math. Mech. 58:3 (1994), 477-485

[32] R.R. Gadyl'shin:
On the scattering of an $H$-polarized electromagnetic field by an ideal conductive cylinder with a narrow lengthwise split of finite depth
Zap. Nauchn. Semin. POMI 210 (1994), 65-72
English transl. J. Math. Sci., New York 83:2 (1997), 204-209

[31] R.R. Gadyl'shin:
On the existence of poles with small imaginary part for a complete electromagnetic analogue of the Helmholtz resonator
Dokl. Akad. Nauk, Ross. Akad. Nauk 338:2 (1994), 151-153
English transl. Russ. Acad. Sci., Dokl., Math. 50:2 (1995), 200-203

[30] R.R. Gadyl'shin:
On scattering by bodies with narrow channels
Mat. Sb. 185:7 (1994), 39-62
English transl. Russ. Acad. Sci., Sb., Math. 82:2 (1995), 293-313

[29] R.R. Gadyl'shin:
On eigenfrequencies of bodies with thin branches. II: Asymptotics
Mat. Zametki 55:1 (1994), 20-34
English transl. Math. Notes 55:1 (1994), 14-23

[28] R.R. Gadyl'shin:
A two-dimensional analog of the Helmholtz resonator with rigid walls
Differ. Uravn. 30:2 (1994), 221-229
English transl. Differ. Equations 30:2 (1994), 201-209

[27] R.R. Gadyl'shin:
Asymptotics of scattering frequencies with small imaginary parts for an acoustic resonator
RAIRO, Modelisation Math. Anal. Numer. 28:6 (1994), 761-780

[26] R.R. Gadyl'shin:
On acoustic Helmholtz resonator and on its electromagnetic analog
J. Math. Phys. 35:7 (1994), 3464-3481

[25] R.R. Gadyl'shin:
On the poles of an acoustic resonator
Funkts. Anal. Prilozh. 27:4 (1993), 3-16
English transl. Funct. Anal. Appl. 27:4 (1993), 229-239

[24] R.R. Gadyl'shin:
Asymptotic behavior of the second eigenfrequency for a system of two bodies connected by a thin rod
Teor. Mat. Fiz. 97:1 (1993), 68-77
English transl. Theor. Math. Phys. 97:1 (1993), 1154-1159

[23] R.R. Gadyl'shin:
The quasi-stationary mode of a Helmholtz resonator
Prikl. Mat. Mekh. 57:5 (1993), 52-59
English transl. J. Appl. Math. Mech. 57:5 (1993), 809-815

[22] R.R. Gadyl'shin:
On scattering frequencies of acoustic resonator
C. R. Acad. Sci., Paris, Ser. I 316:9 (1993), 959-963

[21] R.R. Gadyl'shin:
Characteristic frequencies of bodies with thin spikes. I: Convergence and estimates
Mat. Zametki 54:6 (1993), 10-21
English transl. Math. Notes 54:6 (1993), 1192-1199

[20] R.R. Gadyl'shin:
Splitting a multiple eigenvalue in the boundary value problem for a membrane clamped on a small part of the boundary
Sib. Mat. Zh. 34:3 (1993), 43-61
English transl. Sib. Math. J. 34:3 (1993), 433-450

[19] R.R. Gadyl'shin:
Splitting of the poles of a Helmholtz resonator
Izv. Ross. Akad. Nauk, Ser. Mat. 57:5 (1993), 44-74
English transl. Russ. Acad. Sci., Izv., Math. 43:2 (1994), 233-260

[18] R.R. Gadyl'shin:
The Helmholtz resonator with a small aperture
Zh. Vychisl. Mat. Mat. Fiz. 32:9 (1992), 1464-1475
English transl. Comput. Math. Math. Phys. 32:9 (1992), 1311-1321

[17] R.R. Gadyl'shin:
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
English transl. Math. Notes 52:4 (1992), 1020-1029

[16] R.R. Gadyl'shin:
Coalescent poles of an acoustical resonator
Dokl. Akad. Nauk, Ross. Akad. Nauk 324:4 (1992), 773-776
English transl. Soviet Phys. Dokl. 37:6 (1992), 281-282

[15] R.R. Gadyl'shin:
On a system of imbedded resonators
Dokl. Akad. Nauk, Ross. Akad. Nauk 326:6 (1992), 939-942
English transl. Russ. Acad. Sci., Dokl., Math. 46:2 (1993), 383-386

[14] R.R. Gadyl'shin:
Surface potentials and the method of matching asymptotic expansions in the problem of the Helmholtz resonator
Algebra Anal. 4:2 (1992), 88-115
English transl. St. Petersbg. Math. J. 4:1 (1993), 273-296

[13] R.R. Gadyl'shin:
The method of matched asymptotic expansions in the problem of the Helmholtz acoustic resonator
Prikl. Mat. Mekh. 56:3 (1992), 412-418
English transl. J. Appl. Math. Mech. 56:3 (1992), 340-345

[12] R.R. Gadyl'shin:
Influence of the position of the opening and its shape on the properties of a Helmholtz resonator
Teor. Mat. Fiz. 93:1 (1992), 103-118
English transl. Theor. Math. Phys. 93 (1992), 1151-1159

[11] R.R. Gadyl'shin:
On analytic continuation of the Green's function of a Helmholtz resonator (in Russian)
in "Asymptotic methods for solving differential equations", Ufa 1992; pp. 18-26

[10] R.R. Gadyl'shin:
Scattering $E$--polarized electromagnetic field by an ideally conducting cylindrical surface with a narrow slit
Pis'ma v Zhur. Tekh. Fiz. 18:4 (1992), 10-13
English transl. Soviet Technical Physics Letters. 18:2 (1992) 98-100

[9] R.R. Gadyl'shin:
On splitting of poles of the Green's function for the electromagnetic analogue of a Helmholtz resonator
Radiotekh. i Elektron. 36 (1991), 2045-2047
English transl. Soviet J. Comm. Tech. Electron 37 (1992), ???

[8] R.R. Gadyl'shin:
On asymptotics of an electromagnetic field at the neigborhhood of edge of ideal conductive surface (in Russian)
in "The problems of mathematical physics and asymptotics of their solutions", Ufa 1991; pp. 3-13

[7] R.R. Gadyl'shin:
On the oscillation amplitude for a Helmholtz resonant cavity
Dokl. Akad. Nauk, Ross. Akad. Nauk 310:5 (1990), 1094-1097
English transl. Soviet Phys. Dokl. 35:2 (1990), 141-143

[6] R.R. Gadyl'shin:
On quasi-natural freqiencies of the Helmholtz resonator (in Russian)
in "Asymptotic properties of the solutions of differential equations", Ufa 1990; pp. 33-49

[5] R.R. Gadyl'shin:
Asymptotics of eigenvalues of an elliptic boundary value problem with a small parameter in the boundary conditions (in Russian)
in "Asymptotic methods for solving problems of mathematical physics", Ufa 1989; 24-41

[4] R.R. Gadyl'shin:
The spectrum of elliptic boundary value problems in case of singular perturbations of the boundary conditions (in Russian)
in "Asymptotic properties of the solutions of differential equations", Ufa 1988; pp. 4-16

[3] R.R. Gadyl'shin:
Asymptotic properties of an eigenvalue of a problem for a singularly perturbed self-adjoint elliptic equation with a small parameter in the boundary conditions
Differ. Uravn. 22:4 (1986), 640-652
English transl. Differ. Equations 22 (1986), 474-483

[2] R.R. Gadyl'shin:
A singularly perturbed problem for a Helmholtz operator (in Russian)
in "Differential equations with small parameter", Sverdlovsk 1984; pp. 18-35

[1] R.R. Gadyl'shin:
Asymptotics of a solution the first boundary value problem for an elliptic equation with given singularity at the boundary of the domain (in Russian)
in "Method of matching of asymptotic expansions for problems with singular perturbations", Ufa 1980; pp. 96-114

Preprints

[1] G.A. Chechkin, R.R. Gadyl'shin:
On boundary-value problems for the Laplacian in bounded and in unbounded domains with perforated boundaries
submitted [arXiv:math-ph/0303008; Prepublication du Laboratoire de Mathematiques Appliquees ]

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