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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

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Abstract

In a separable Hilbert space \(H\), 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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Funding

This work was supported by the Science Development Foundation under the President of Republic of Azerbaijan, project no. EIF/MQM/Elm Tehsil-1-2016-1(26)-71/10/1.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AZ1141, Azerbaijan

    B. A. Aliev

  2. Azerbaijan State Pedagogical University, Baku, 370000, Azerbaijan

    B. A. Aliev & V. Z. Kerimov

Authors
  1. B. A. Aliev
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  2. V. Z. Kerimov
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Corresponding authors

Correspondence to B. A. Aliev or V. Z. Kerimov.

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Translated by V. Potapchouck

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Aliev, B.A., Kerimov, V.Z. 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. Diff Equat 56, 190–198 (2020). https://doi.org/10.1134/S0012266120020056

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