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Research Article | Open Access

Eigenvalues of fourth-order boundary value problems with distributional potentials

Hai-yan Zhang1, Ji-jun Ao1( ), Fang-zhen Bo2
College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
Normal College, Hohhot Vocational College, Hohhot 010051, China
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Abstract

This paper aims to investigate the fourth-order boundary value problems with distributional potentials. We first prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Then we obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problems: the boundary conditions, the coefficient functions and the endpoints. Moreover, we find the differential expressions for each parameter.

Keywords

fourth-order boundary value problemsdistributional potentialsquasi-derivativeseigenvalues
CLC number: 34B09, 34L10, 34B05, 47A75

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7294-7317
DOI: 10.3934/math.2022407

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Cite this article:
Zhang H-y, Ao J-j, Bo F-z. Eigenvalues of fourth-order boundary value problems with distributional potentials. AIMS Mathematics, 2022, 7(5): 7294-7317. https://doi.org/10.3934/math.2022407

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Received: 10 November 2021
Revised: 21 January 2022
Accepted: 29 January 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)