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

In a separable Hilbert space , we study the asymptotic behavior of eigenvalues of a boundary value problem for second-order elliptic differential–operator equations for the case in which the spectral parameter occurs in the equation quadratically and one of the boundary conditions is a quadratic tri...

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Bibliographic Details
Published in:Differential equations Vol. 56; no. 2; pp. 190 - 198
Main Authors: Aliev, B. A., Kerimov, V. Z.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.02.2020
Springer
Springer Nature B.V
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ISSN:0012-2661, 1608-3083
Online Access:Get full text
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Summary:In a separable Hilbert space , we study the asymptotic behavior of eigenvalues of a boundary value problem for second-order elliptic differential–operator equations for the case in which the spectral parameter occurs in the equation quadratically and one of the boundary conditions is a quadratic trinomial in the same spectral parameter. We derive asymptotic formulas for the eigenvalues of this boundary value problem. An application of the abstract results obtained here to elliptic boundary value problems is indicated.
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content type line 14
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266120020056