Asymptotic Behavior of Eigenvalues of a Boundary Value Problem for a Second-Order Elliptic Differential-Operator Equation with Spectral Parameter Quadratically Occurring in the Boundary Condition

The asymptotic behavior of eigenvalues of a boundary value problem for a secondorder differential-operator equation in a separable Hilbert space on a finite interval is studied for the case in which the same spectral parameter occurs linearly in the equation and quadratically in one of the boundary...

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Vydané v:	Differential equations Ročník 54; číslo 9; s. 1256 - 1260
Hlavný autor:	Aliev, B. A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Moscow Pleiades Publishing 01.09.2018 Springer Springer Nature B.V
Predmet:	Asymptotic properties Boundary conditions Boundary value problems Difference and Functional Equations Differential equations Economic models Eigenvalues Hilbert space Mathematics Mathematics and Statistics Ordinary Differential Equations Parameters Partial Differential Equations Short Communications
ISSN:	0012-2661, 1608-3083
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Abstract	The asymptotic behavior of eigenvalues of a boundary value problem for a secondorder differential-operator equation in a separable Hilbert space on a finite interval is studied for the case in which the same spectral parameter occurs linearly in the equation and quadratically in one of the boundary conditions. We prove that the problem has a sequence of eigenvalues converging to zero.
AbstractList	The asymptotic behavior of eigenvalues of a boundary value problem for a secondorder differential-operator equation in a separable Hilbert space on a finite interval is studied for the case in which the same spectral parameter occurs linearly in the equation and quadratically in one of the boundary conditions. We prove that the problem has a sequence of eigenvalues converging to zero.
Audience	Academic
Author	Aliev, B. A.
Author_xml	– sequence: 1 givenname: B. A. surname: Aliev fullname: Aliev, B. A. email: aliyevbakhram@yandex.ru organization: Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku State Pedagogical University
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Cites_doi	10.1134/S001226611110003X 10.1007/s11253-006-0134-1 10.1007/BF01092795 10.1134/S001226610910019X
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Copyright	Pleiades Publishing, Ltd. 2018 COPYRIGHT 2018 Springer Differential Equations is a copyright of Springer, (2018). All Rights Reserved.
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References	Gorbachuk, Rybak (CR2) 1981 Aliev, Kurbanova, Yakubov (CR6) 2015; 6 Aliev, Kurbanova (CR5) 2014 Kapustin (CR7) 2009; 45 Aliev (CR4) 2006; 58 Yakubov (CR1) 1982; 26 Rybak (CR3) 1980; 32 Kapustin (CR8) 2011; 47 V.I. Gorbachuk (723_CR2) 1981 N.Yu. Kapustin (723_CR7) 2009; 45 B.A. Aliev (723_CR4) 2006; 58 B.A. Aliev (723_CR6) 2015; 6 M.A. Rybak (723_CR3) 1980; 32 S.Ya. Yakubov (723_CR1) 1982; 26 B.A. Aliev (723_CR5) 2014 N.Yu. Kapustin (723_CR8) 2011; 47
References_xml	– year: 1981 ident: CR2 article-title: On the boundary value problems for the operator Sturm–Liouville equation with a spectral parameter in the equation and in the boundary condition publication-title: Direct and Inverse Problems of Scattering Theory – year: 2014 ident: CR5 article-title: Asymptotic behavior of eigenvalues of a boundary value problem for a second order elliptic differential-operator equation publication-title: Proc. Inst. Math. Mech.: Natl. Acad. Sci. Azerb. – volume: 6 start-page: 241 year: 2015 end-page: 265 ident: CR6 article-title: Solvability of the abstract Regge boundary value problem and asymptotic behavior of eigenvalues of one abstract spectral problem publication-title: Riv. Mat. Univ. Parma – volume: 26 start-page: 276 year: 1982 end-page: 279 ident: CR1 article-title: A boundary value problem for the Laplace equation with nonclassical spectral asymptotics publication-title: Sov. Math. Dokl. – volume: 47 start-page: 1408 issue: 10 year: 2011 end-page: 1413 ident: CR8 article-title: On the uniform convergence in C1 of Fourier series for a spectral problem with squared spectral parameter in a boundary condition publication-title: Differ. Equations doi: 10.1134/S001226611110003X – volume: 58 start-page: 1298 issue: 8 year: 2006 end-page: 1306 ident: CR4 article-title: Asymptotic behavior of the eigenvalues of a boundary value problem for a second-order elliptic operator-differential equation publication-title: Ukr. Math. J. doi: 10.1007/s11253-006-0134-1 – volume: 32 start-page: 159 year: 1980 end-page: 162 ident: CR3 article-title: Asymptotic distribution of the eigenvalues of some boundary value problems for Sturm–Liouville operator equations publication-title: Ukr. Math. J. doi: 10.1007/BF01092795 – volume: 45 start-page: 1509 issue: 10 year: 2009 end-page: 1511 ident: CR7 article-title: On a spectral problem in the theory of the heat operator publication-title: Differ. Equations doi: 10.1134/S001226610910019X – volume: 58 start-page: 1298 issue: 8 year: 2006 ident: 723_CR4 publication-title: Ukr. Math. J. doi: 10.1007/s11253-006-0134-1 – volume: 6 start-page: 241 year: 2015 ident: 723_CR6 publication-title: Riv. Mat. Univ. Parma – volume-title: Direct and Inverse Problems of Scattering Theory year: 1981 ident: 723_CR2 – volume: 32 start-page: 159 year: 1980 ident: 723_CR3 publication-title: Ukr. Math. J. doi: 10.1007/BF01092795 – volume: 26 start-page: 276 year: 1982 ident: 723_CR1 publication-title: Sov. Math. Dokl. – volume-title: Proc. Inst. Math. Mech.: Natl. Acad. Sci. Azerb. year: 2014 ident: 723_CR5 – volume: 45 start-page: 1509 issue: 10 year: 2009 ident: 723_CR7 publication-title: Differ. Equations doi: 10.1134/S001226610910019X – volume: 47 start-page: 1408 issue: 10 year: 2011 ident: 723_CR8 publication-title: Differ. Equations doi: 10.1134/S001226611110003X
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SubjectTerms	Asymptotic properties Boundary conditions Boundary value problems Difference and Functional Equations Differential equations Economic models Eigenvalues Hilbert space Mathematics Mathematics and Statistics Ordinary Differential Equations Parameters Partial Differential Equations Short Communications
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Title	Asymptotic Behavior of Eigenvalues of a Boundary Value Problem for a Second-Order Elliptic Differential-Operator Equation with Spectral Parameter Quadratically Occurring in the Boundary Condition
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