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2004•Izvestiya MathematicsRequires access

On a fourth-order problem with spectral and physical parameters in the boundary condition

Jamel Ben Amara, А. А. Vladimirov

Open publisher page 16 citations

Abstract

We consider the following fourth-order boundary-value problem: with spectral parameter and physical parameter . We assign to this problem a linear pencil of bounded operators depending on the physical parameter and acting from to the dual space . We study the spectral properties of and use the results of this study to describe properties of the eigenvalues of the problem for various values of . In particular, we establish asymptotics of these eigenvalues as .

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What this paper is about

We consider the following fourth-order boundary-value problem: with spectral parameter and physical parameter . We assign to this problem a linear pencil of bounded operators depending on the physical parameter and acting from to the dual space . We study the spectral properties of and use the results of this study to describe properties of the eigenvalues of the problem for various values of . In particular, we establish asymptotics of these eigenvalues as .

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OpenAlex reports 16 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We consider the following fourth-order boundary-value problem: with spectral parameter and physical parameter . We assign to this problem a linear pencil of bounded operators depending on the physical parameter and acting from to the dual space . We study the spectral properties of and use the results of this study to describe properties of the eigenvalues of the problem for various values of . In particular, we establish asymptotics of these eigenvalues as .

Key concepts: Boundary value problem, Order (exchange), Mathematics, Applied mathematics, Mathematical analysis, Economics, Finance

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