Gadyl’shin, R. R.; Piatnitskii, A. L.; Chechkin, G. A. On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type. (English. Russian original) Zbl 1406.35032 Izv. Math. 82, No. 6, 1108-1135 (2018); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 6, 37-64 (2018). MSC: 35B27 35C20 35J05 35J25 35P15 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} et al., Izv. Math. 82, No. 6, 1108--1135 (2018; Zbl 1406.35032); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 6, 37--64 (2018) Full Text: DOI
Gadyl’shin, R. R.; Rep’evskii, S. V.; Shishkina, E. A. 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. (English. Russian original) Zbl 1345.35019 Proc. Steklov Inst. Math. 292, Suppl. 1, S76-S90 (2016); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 21, No. 1, 56-70 (2015). Reviewer: Patrick Winkert (Berlin) MSC: 35J05 35P15 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} et al., Proc. Steklov Inst. Math. 292, S76--S90 (2016; Zbl 1345.35019); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 21, No. 1, 56--70 (2015) Full Text: DOI
Gadyl’shin, R. R.; Koroleva, Yu. O.; Chechkin, G. A. On the eigenvalue of the Laplacian in a domain perforated along the boundary. (English. Russian original) Zbl 1205.35171 Dokl. Math. 81, No. 3, 337-341 (2010); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 432, No. 1, 7-11 (2010). MSC: 35P05 35J05 35B25 35C20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} et al., Dokl. Math. 81, No. 3, 337--341 (2010; Zbl 1205.35171); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 432, No. 1, 7--11 (2010) Full Text: DOI
Amirat, Youcef; Chechkin, Gregory A.; Gadyl’shin, Rustem R. Spectral boundary homogenization in domains with oscillating boundaries. (English) Zbl 1204.35035 Nonlinear Anal., Real World Appl. 11, No. 6, 4492-4499 (2010). Reviewer: Adrian Muntean (Eindhoven) MSC: 35B27 35P05 35J05 35J25 PDFBibTeX XMLCite \textit{Y. Amirat} et al., Nonlinear Anal., Real World Appl. 11, No. 6, 4492--4499 (2010; Zbl 1204.35035) Full Text: DOI
Gadyl’shin, R. R. On regular and singular perturbations of the eigenelements of the Laplacian. (English) Zbl 1221.35110 Constanda, C. (ed.) et al., Integral methods in science and engineering. Volume 1: Analytic methods. Papers presented at the 10th international conference on integral methods in science and engineering (IMSE 2008), Santander, Spain, July 7–10, 2008. Basel: Birkhäuser (ISBN 978-0-8176-4898-5/hbk; 978-0-8176-4899-2/ebook). 135-148 (2010). Reviewer: Luis Filipe Pinheiro de Castro (Aveiro) MSC: 35J05 35B20 35B25 35C20 35J10 35P15 47F05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, in: Integral methods in science and engineering. Volume 1: Analytic methods. Papers presented at the 10th international conference on integral methods in science and engineering (IMSE 2008), Santander, Spain, July 7--10, 2008. Basel: Birkhäuser. 135--148 (2010; Zbl 1221.35110) Full Text: DOI
Amirat, Youcef; Chechkin, Gregory A.; Gadyl’shin, Rustem R. Asymptotics of the solution of a Dirichlet spectral problem in a junction with highly oscillating boundary. (English) Zbl 1145.35359 C. R., Méc., Acad. Sci. Paris 336, No. 9, 693-698 (2008). MSC: 35J05 35B10 PDFBibTeX XMLCite \textit{Y. Amirat} et al., C. R., Méc., Acad. Sci. Paris 336, No. 9, 693--698 (2008; Zbl 1145.35359) Full Text: DOI
Amirat, Y.; Chechkin, G. A.; Gadyl’shin, R. R. Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operatorl in a domain with an oscillating boundary. (English) Zbl 1210.35032 Zh. Vychisl. Mat. Mat. Fiz. 46, No. 1, 102-115 (2006); translation in Comput. Math. Math. Phys. 46, No. 1, 97-110 (2006). MSC: 35J05 PDFBibTeX XMLCite \textit{Y. Amirat} et al., Zh. Vychisl. Mat. Mat. Fiz. 46, No. 1, 102--115 (2006; Zbl 1210.35032); translation in Comput. Math. Math. Phys. 46, No. 1, 97--110 (2006)
Gadyl’shin, R. R. On the eigenvalues of a “dumbbell with a thin handle”. (English. Russian original) Zbl 1075.35023 Izv. Math. 69, No. 2, 265-329 (2005); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 2, 45-110 (2005). MSC: 35P20 35C20 35J05 35B25 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Izv. Math. 69, No. 2, 265--329 (2005; Zbl 1075.35023); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 2, 45--110 (2005) Full Text: DOI
Gadyl’shin, R. R. On domains with a narrow isthmus in the critical case. (English) Zbl 1126.35346 Danilin, A. R. (ed.), Asymptotic expansions, approximation theory, topology. Transl. from the Russian. Moscow: Maik Nauka / Interperiodica. Proceedings of the Steklov Institute of Mathematics 2003, Suppl. 1, S68-S74 (2003). MSC: 35P20 34L15 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, in: Asymptotic expansions, approximation theory, topology. Transl. from the Russian. Moscow: Maik Nauka / Interperiodica. S68--S74 (2003; Zbl 1126.35346)
Gadyl’shin, R. R. Scattering by a cylindrical trap in the critical case. (English. Russian original) Zbl 1054.35045 Math. Notes 73, No. 3, 328-341 (2003); translation from Mat. Zametki 73, No. 3, 355-370 (2003). MSC: 35P25 35J05 76Q05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Math. Notes 73, No. 3, 328--341 (2003; Zbl 1054.35045); translation from Mat. Zametki 73, No. 3, 355--370 (2003) Full Text: DOI arXiv
Gadyl’shin, R. R. Eigenvalues of the Neumann problem in a domain with a thin channel. (English. Russian original) Zbl 1146.35336 Dokl. Math. 66, No. 3, 436-439 (2002); translation from Dokl. Akad. Nauk 387, No. 1, 26-30 (2002). Reviewer: Andrei Zemskov (Moskva) MSC: 35J05 35P05 35P15 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Dokl. Math. 66, No. 3, 436--439 (2002; Zbl 1146.35336); translation from Dokl. Akad. Nauk 387, No. 1, 26--30 (2002)
Gadyl’shin, R. R. On analogues of the Helmholtz resonator in averaging theory. (English. Russian original) Zbl 1085.35023 Sb. Math. 193, No. 11, 1611-1638 (2002); translation from Mat. Sb. 193, No. 11, 43-70 (2002). Reviewer: Marco Biroli (Milano) MSC: 35B27 35J05 35C20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Sb. Math. 193, No. 11, 1611--1638 (2002; Zbl 1085.35023); translation from Mat. Sb. 193, No. 11, 43--70 (2002) Full Text: DOI
Gadyl’shin, R. R. On a model analogue of the Helmholtz resonator in homogenization. (English. Russian original) Zbl 1022.35003 Proc. Steklov Inst. Math. 236, 70-77 (2002); translation from Tr. Mat. Inst. Steklova 236, 79-86 (2002). Reviewer: Alexander A.Kovalevsky (Donetsk) MSC: 35B27 35J05 35J25 35B34 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, in: Differential equations and dynamical systems. Collected papers dedicated to the 80th birthday of Academician Evgenii Frolovich Mishchenko. Transl. from the Russian. Moscow: Maik Nauka/Interperiodika. 70--77 (2002; Zbl 1022.35003); translation from Tr. Mat. Inst. Steklova 236, 79--86 (2002)
Borisov, D.; Exner, P.; Gadyl’shin, R.; Krejčiřík, D. Bound states in weakly deformed strips and layers. (English) Zbl 1043.35046 Ann. Henri Poincaré 2, No. 3, 553-572 (2001). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35C20 35P05 35J05 PDFBibTeX XMLCite \textit{D. Borisov} et al., Ann. Henri Poincaré 2, No. 3, 553--572 (2001; Zbl 1043.35046) Full Text: DOI arXiv
Gadyl’shin, R. R. Resonator systems. (English. Russian original) Zbl 0972.35080 Izv. Math. 64, No. 3, 487-529 (2000); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, No. 3, 51-96 (2000). Reviewer: V.A.Liskevich (Bristol) MSC: 35P25 47A40 35C20 35J05 35J10 35J25 35B99 76Q05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Izv. Math. 64, No. 3, 487--529 (2000; Zbl 0972.35080); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, No. 3, 51--96 (2000) Full Text: DOI
Gadyl’shin, R. R. On the Dirichlet problem for the Helmholtz equation on the plane with boundary conditions on an almost closed curve. (English. Russian original) Zbl 0982.35033 Sb. Math. 191, No. 6, 821-848 (2000); translation from Mat. Sb. 191, No. 6, 43-68 (2000). Reviewer: N.Weck (Essen) MSC: 35J05 35J25 35B25 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Sb. Math. 191, No. 6, 43--68 (2000; Zbl 0982.35033); translation from Mat. Sb. 191, No. 6, 43--68 (2000) Full Text: DOI
Gadyl’shin, R. R. Asymptotics of the eigenvalues of a boundary value problem with rapidly oscillating boundary conditions. (English. Russian original) Zbl 1158.35399 Differ. Equations 35, No. 4, 540-551 (1999); translation from Differ. Uravn. 35, No. 4, 540-551 (1999). MSC: 35P20 35B25 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Differ. Equations 35, No. 4, 540--551 (1999; Zbl 1158.35399); translation from Differ. Uravn. 35, No. 4, 540--551 (1999)
Borisov, D. I.; Gadyl’shin, R. R. On the spectrum of the Laplacian with frequently alternating boundary conditions. (English. Russian original) Zbl 0945.35066 Theor. Math. Phys. 118, No. 3, 272-277 (1999); translation from Teor. Mat. Fiz. 118, No. 3, 347-353 (1999). MSC: 35P05 35J05 35B25 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{R. R. Gadyl'shin}, Theor. Math. Phys. 118, No. 3, 272--277 (1999; Zbl 0945.35066); translation from Teor. Mat. Fiz. 118, No. 3, 347--353 (1999) Full Text: DOI
Gadyl’shin, R. R.; Chechkin, G. A. A boundary value problem for the Laplacian with rapidly changing type of boundary conditions in a multidimensional domain. (English. Russian original) Zbl 0939.35048 Sib. Math. J. 40, No. 2, 229-244 (1999); translation from Sib. Mat. Zh. 40, No. 2, 271-287 (1999). Reviewer: V.Grebenev (Novosibirsk) MSC: 35J05 35J25 35B05 35B40 35P20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} and \textit{G. A. Chechkin}, Sib. Math. J. 40, No. 2, 229--244 (1999; Zbl 0939.35048); translation from Sib. Mat. Zh. 40, No. 2, 271--287 (1999)
Gadyl’shin, Rustem R. On an analog of the Helmholtz resonator in the averaging theory. (English. Abridged French version) Zbl 0938.35040 C. R. Acad. Sci., Paris, Sér. I, Math. 329, No. 12, 1121-1126 (1999). MSC: 35J05 35B40 35B60 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, C. R. Acad. Sci., Paris, Sér. I, Math. 329, No. 12, 1121--1126 (1999; Zbl 0938.35040) Full Text: DOI
Gadyl’shin, R. R. A system of embedded resonators. (English. Russian original) Zbl 0967.35033 Transl., Ser. 2, Am. Math. Soc. 193, 27-44 (1999); translation from Tr. St. Peterbg. Mat. Obshch. 5, 43-68 (1998). Reviewer: Ll.G.Chambers (Bangor) MSC: 35J05 35B60 35C20 35P25 78A45 76Q05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Transl., Ser. 2, Am. Math. Soc. 193, 1 (1998; Zbl 0967.35033); translation from Tr. St. Peterbg. Mat. Obshch. 5, 43--68 (1998)
Gadyl’shin, R. R. On the eigenvalue asymptotics for periodically clamped membranes. (English. Russian original) Zbl 0907.35094 St. Petersbg. Math. J. 10, No. 1, 1-14 (1999); translation from Algebra Anal. 10, No. 1, 3-19 (1998). Reviewer: O.Titow (Berlin) MSC: 35P20 35B27 35J05 35B20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, St. Petersbg. Math. J. 10, No. 1, 3--19 (1998; Zbl 0907.35094); translation from Algebra Anal. 10, No. 1, 3--19 (1998)
Gadyl’shin, R. R. Characteristic frequencies of bodies with thin spikes. III: Frequency splitting. (English. Russian original) Zbl 0917.35085 Math. Notes 61, No. 4, 409-416 (1997); translation from Mat. Zametki 61, No. 4, 494-502 (1997). MSC: 35P20 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Math. Notes 61, No. 4, 409--416 (1997; Zbl 0917.35085); translation from Mat. Zametki 61, No. 4, 494--502 (1997) Full Text: DOI
Gadyl’shin, R. R. Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator. (English. Russian original) Zbl 0902.35025 Russ. Math. Surv. 52, No. 1, 1-72 (1997); translation from Usp. Mat. Nauk 52, No. 1, 3-76 (1997). Reviewer: Akira Kaneko (Otsuka) MSC: 35J05 35C20 76Q05 35B40 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Russ. Math. Surv. 52, No. 1, 1--72 (1997; Zbl 0902.35025); translation from Usp. Mat. Nauk 52, No. 1, 3--76 (1997) Full Text: DOI
Gadyl’shin, Rustem R. Asymptotics of the minimum eigenvalue for a circle with fast oscillating boundary conditions. (English. Abridged French version) Zbl 0858.35028 C. R. Acad. Sci., Paris, Sér. I 323, No. 3, 319-323 (1996). MSC: 35J25 35P05 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, C. R. Acad. Sci., Paris, Sér. I 323, No. 3, 319--323 (1996; Zbl 0858.35028)
Gadyl’shin, R. R. On the perturbation of the Laplacian spectrum when the boundary condition type changes on a small part of the boundary. (English. Russian original) Zbl 1161.35311 Comput. Math. Math. Phys. 36, No. 7, 889-898 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 7, 77-88 (1996). MSC: 35B25 35C20 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Comput. Math. Math. Phys. 36, No. 7, 889--898 (1996; Zbl 1161.35311); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 7, 77--88 (1996)
Gadyl’shin, R. R. Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem. (English. Russian original) Zbl 1027.35500 Comput. Math. Math. Phys. 36, No. 1, 75-84 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz 36, No. 1, 92-102 (1996). MSC: 35B25 35C20 35J05 76Q05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Comput. Math. Math. Phys. 36, No. 1, 75--84 (1996; Zbl 1027.35500); translation from Zh. Vychisl. Mat. Mat. Fiz 36, No. 1, 92--102 (1996)
Gadyl’shin, R. R. On scattering by a cylinder with a narrow slit and walls of finite thickness. (English. Russian original) Zbl 0889.35073 Theor. Math. Phys. 106, No. 1, 19-34 (1996); translation from Teor. Mat. Fiz. 106, No. 1, 24-43 (1996). MSC: 35P25 35J05 76Q05 35C20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Theor. Math. Phys. 106, No. 1, 19--34 (1996; Zbl 0889.35073); translation from Teor. Mat. Fiz. 106, No. 1, 24--43 (1996) Full Text: DOI
Gadyl’shin, R. R. Scattering on a cylindrical surface with a narrow gap. (English. Russian original) Zbl 0897.35059 Differ. Equations 32, No. 10, 1358-1367 (1996); translation from Differ. Uravn. 32, No. 10, 1362-1370 (1996). Reviewer: V.Chernyatin (Szczecin) MSC: 35P25 35J05 35J25 35C20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Differ. Equations 32, No. 10, 1358--1367 (1996; Zbl 0897.35059); translation from Differ. Uravn. 32, No. 10, 1362--1370 (1996)
Gadyl’shin, R. R. On scattering of polarized electromagnetic field by ideal conductive cylinder with narrow slit. (English) Zbl 0858.35121 Kalyakin, L. A. (ed.) et al., Asymptotics and symmetries in nonlinear dynamical systems. Ufa: Institut Matematiki s Vychislitel’nym Tsentrom RAN. 105-119 (1995). MSC: 35Q60 78A45 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, in: Asimptotiki i simmetrii v nelinejnykh dinamicheskikh sistemakh. Ufa: Institut Matematiki s Vychislitel'nym Tsentrom RAN. 105--119 (1995; Zbl 0858.35121)
Gadyl’shin, R. R. On the scattering of an \(H\)-polarized electromagnetic field by an ideal conductive cylinder with a narrow lengthwise split of finite depth. (English. Russian original) Zbl 0872.35113 J. Math. Sci., New York 83, No. 2, 204-209 (1997); translation from Zap. Nauchn. Semin. POMI 210, 65-72 (1994). MSC: 35Q60 78A45 35P10 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, J. Math. Sci., New York 83, No. 1, 65--72 (1994; Zbl 0872.35113); translation from Zap. Nauchn. Semin. POMI 210, 65--72 (1994) Full Text: DOI EuDML
Gadyl’shin, R. R. On scattering by bodies with narrow channels. (English. Russian original) Zbl 0840.35024 Russ. Acad. Sci., Sb., Math. 82, No. 2, 293-313 (1995); translation from Mat. Sb. 185, No. 7, 39-62 (1994). Reviewer: Ya.A.Rojtberg (Chernigov) MSC: 35J05 78A25 35A20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Russ. Acad. Sci., Sb., Math. 82, No. 2, 39--62 (1994; Zbl 0840.35024); translation from Mat. Sb. 185, No. 7, 39--62 (1994) Full Text: DOI
Gadyl’shin, R. R. On eigenfrequencies of bodies with thin branches. II: Asymptotics. (English. Russian original) Zbl 0839.35091 Math. Notes 55, No. 1, 14-23 (1994); translation from Mat. Zametki 55, No. 1, 20-34 (1994). MSC: 35P20 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Math. Notes 55, No. 1, 1 (1994; Zbl 0839.35091); translation from Mat. Zametki 55, No. 1, 20--34 (1994) Full Text: DOI
Gadyl’shin, R. R. A two-dimensional analog of the Helmholtz resonator with rigid walls. (English. Russian original) Zbl 0824.35029 Differ. Equations 30, No. 2, 201-209 (1994); translation from Differ. Uravn. 30, No. 2, 221-229 (1994). Reviewer: V.Chernyatin (Szczecin) MSC: 35J05 35P25 35J67 47A40 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Differ. Equations 30, No. 2, 1 (1994; Zbl 0824.35029); translation from Differ. Uravn. 30, No. 2, 221--229 (1994)
Gadyl’shin, Rustem R. On acoustic Helmholtz resonator and on its electromagnetic analog. (English) Zbl 0817.35018 J. Math. Phys. 35, No. 7, 3464-3481 (1994). MSC: 35J05 78A25 35C20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, J. Math. Phys. 35, No. 7, 3464--3481 (1994; Zbl 0817.35018) Full Text: DOI
Gadyl’shin, R. R. On the scattering of an \(H\)-polarized electromagnetic field by an ideal conductive cylinder with a narrow lengthwise split of finite depth. (Russian. English summary) Zbl 0869.35098 Zap. Nauchn. Semin. POMI 210, 65-72 (1994). MSC: 35Q60 78A45 35P10 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Zap. Nauchn. Semin. POMI 210, 65--72 (1994; Zbl 0869.35098) Full Text: EuDML
Gadyl’shin, R. R. Systems of acoustic resonators in the quasistationary mode. (English. Russian original) Zbl 0881.76086 J. Appl. Math. Mech. 58, No. 3, 477-485 (1994); translation from Prikl. Mat. Mekh. 58, No. 3, 104-112 (1994). MSC: 76Q05 35J05 35C20 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, J. Appl. Math. Mech. 58, No. 3, 477--485 (1994; Zbl 0881.76086); translation from Prikl. Mat. Mekh. 58, No. 3, 104--112 (1994) Full Text: DOI
Gadyl’shin, R. R. Characteristic frequencies of bodies with thin spikes. I: Convergence and estimates. (English. Russian original) Zbl 0829.35088 Math. Notes 54, No. 6, 1192-1199 (1993); translation from Mat. Zametki 54, No. 6, 10-21 (1993). MSC: 35P20 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Math. Notes 54, No. 6, 1 (1993; Zbl 0829.35088); translation from Mat. Zametki 54, No. 6, 10--21 (1993) Full Text: DOI
Gadyl’shin, R. R. Splitting of the poles of a Helmholtz resonator. (English. Russian original) Zbl 0827.35095 Russ. Acad. Sci., Izv., Math. 43, No. 2, 233-260 (1994); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 5, 44-74 (1993). MSC: 35P25 35J05 78A45 70K30 47A40 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Russ. Acad. Sci., Izv., Math. 43, No. 2, 1 (1993; Zbl 0827.35095); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 5, 44--74 (1993) Full Text: DOI
Gadyl’shin, R. R. Splitting a multiple eigenvalue in the boundary value problem for a membrane clamped on a small part of the boundary. (English. Russian original) Zbl 0827.35082 Sib. Math. J. 34, No. 3, 433-450 (1993); translation from Sib. Mat. Zh. 34, No. 3, 43-61 (1993). Reviewer: G.Bottaro (Genova) MSC: 35P05 35J05 35P10 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Sib. Math. J. 34, No. 3, 43--61 (1993; Zbl 0827.35082); translation from Sib. Mat. Zh. 34, No. 3, 43--61 (1993) Full Text: DOI
Gadyl’shin, R. R. Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition. (English. Russian original) Zbl 0816.35093 Math. Notes 52, No. 4, 1020-1029 (1992); translation from Mat. Zametki 52, No. 4, 42-55 (1992). MSC: 35P15 35J05 35B25 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Math. Notes 52, No. 4, 1 (1992; Zbl 0816.35093); translation from Mat. Zametki 52, No. 4, 42--55 (1992) Full Text: DOI
Gadyl’shin, R. R. Surface potentials and the method of matching of asymptotic expansions in the Helmholtz resonator problem. (Russian) Zbl 0787.35024 Algebra Anal. 4, No. 2, 88-115 (1992). Reviewer: D.M.Bors (Iaşi) MSC: 35J05 35P25 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Algebra Anal. 4, No. 2, 88--115 (1992; Zbl 0787.35024)
Gadyl’shin, R. R. The Helmholtz resonator with a small aperture. (English. Russian original) Zbl 0830.35019 Comput. Math. Math. Phys. 32, No. 9, 1311-1321 (1992); translation from Zh. Vychisl. Mat. Mat. Fiz. 32, No. 9, 1464-1475 (1992). MSC: 35C20 35J05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Comput. Math. Math. Phys. 32, No. 9, 1464--1475 (1992; Zbl 0830.35019); translation from Zh. Vychisl. Mat. Mat. Fiz. 32, No. 9, 1464--1475 (1992)
Gadyl’shin, R. R. Surface potentials and the method of matching asymptotic expansions in the problem of the Helmholtz resonator. (English. Russian original) Zbl 0792.35031 St. Petersbg. Math. J. 4, No. 1, 273-296 (1993); translation from Algebra Anal. 4, No. 2, 88-115 (1992). MSC: 35J05 35P25 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, St. Petersbg. Math. J. 4, No. 1, 273--296 (1992; Zbl 0792.35031); translation from Algebra Anal. 4, No. 2, 88--115 (1992)
Gadyl’shin, R. R. A singularly perturbed problem for a Helmholtz operator. (Russian) Zbl 0581.35011 Differential equations with small parameter, Collect. Artic., Sverdlovsk 1984, 18-35 (1984). Reviewer: K.Barckow MSC: 35J05 35B25 35C20 PDFBibTeX XML