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.; Kozhevnikov, D. V.; Chechkin, G. A. Spectral problem in a domain perforated along the boundary. Perturbation of a multiple eigenvalue. (English. Russian original) Zbl 1301.35071 J. Math. Sci., New York 196, No. 3, 276-292 (2014); translation from Probl. Mat. Anal. 73, 31-45 (2013). MSC: 35P20 35J20 35B27 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} et al., J. Math. Sci., New York 196, No. 3, 276--292 (2014; Zbl 1301.35071); translation from Probl. Mat. Anal. 73, 31--45 (2013) Full Text: DOI
Gadyl’shin, R. R.; Shishkina, E. A. On Friedrichs inequalities for a disk. (English. Russian original) Zbl 1295.26019 Proc. Steklov Inst. Math. 281, Suppl. 1, S44-S58 (2013); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 48-61 (2012). Reviewer: Qingkai Kong (DeKalb) MSC: 26D10 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} and \textit{E. A. Shishkina}, Proc. Steklov Inst. Math. 281, S44--S58 (2013; Zbl 1295.26019); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 48--61 (2012) Full Text: DOI
Gadyl’shin, Rustem R.; Il’in, Arlen M. On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit. (English) Zbl 1200.35081 Asymptotic Anal. 67, No. 3-4, 167-189 (2010). MSC: 35J25 35P05 35C20 35P15 35B25 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} and \textit{A. M. Il'in}, Asymptotic Anal. 67, No. 3--4, 167--189 (2010; Zbl 1200.35081) Full Text: DOI arXiv
Amirat, Youcef; Chechkin, Gregory A.; Gadyl’shin, Rustem R. Asymptotic approximation of eigenelements of the Dirichlet problem for the Laplacian in a domain with shoots. (English) Zbl 1200.35020 Math. Methods Appl. Sci. 33, No. 7, 811-830 (2010). MSC: 35B27 76M50 35P05 35C20 35J25 PDFBibTeX XMLCite \textit{Y. Amirat} et al., Math. Methods Appl. Sci. 33, No. 7, 811--830 (2010; Zbl 1200.35020) Full Text: DOI
Borisov, D. I.; Gadyl’shin, R. R. On the spectrum of a periodic operator with a small localized perturbation. (English. Russian original) Zbl 1169.34056 Izv. Math. 72, No. 4, 659-688 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 4, 37-66 (2008). Reviewer: Amin Boumenir (Carrollton) MSC: 34L05 47E05 34E10 34L40 47A10 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{R. R. Gadyl'shin}, Izv. Math. 72, No. 4, 659--688 (2008; Zbl 1169.34056); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 4, 37--66 (2008) Full Text: DOI arXiv
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, Rustem R. On resonances in a homogenization problem. (English. French summary) Zbl 1223.74033 C. R., Méc., Acad. Sci. Paris 331, No. 9, 595-600 (2003). MSC: 74Q05 35Q74 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, C. R., Méc., Acad. Sci. Paris 331, No. 9, 595--600 (2003; Zbl 1223.74033) Full Text: DOI
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 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)
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, 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. 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, R. R.; Kiselev, O. M. On the soliton-free structure of scattering data on perturbation of a two-dimensional soliton for the Davey-Stewartson equation II. (English. Russian original) Zbl 0889.35098 Theor. Math. Phys. 106, No. 2, 167-173 (1996); translation from Teor. Mat. Fiz. 106, No. 2, 200-208 (1996). MSC: 35Q55 35A22 35P25 35R30 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin} and \textit{O. M. Kiselev}, Theor. Math. Phys. 106, No. 2, 167--173 (1996; Zbl 0889.35098); translation from Teor. Mat. Fiz. 106, No. 2, 200--208 (1996) 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. (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 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. 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, Rustem R. On scattering frequencies of acoustic resonator. (English. Abridged French version) Zbl 0774.76071 C. R. Acad. Sci., Paris, Sér. I 316, No. 9, 959-963 (1993). MSC: 76Q05 PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, C. R. Acad. Sci., Paris, Sér. I 316, No. 9, 959--963 (1993; Zbl 0774.76071)