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Research Article | Open Access

Eigenvalues of fourth-order differential operators with eigenparameter dependent boundary conditions

Jianfang Qin, Kun Li, Zhaowen Zheng( ), Jinming Cai
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
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Abstract

This paper is concerned with a fourth-order differential operator with eigenparameter dependent boundary conditions. We prove that each of the eigenvalues of the problem can be embedded in a continuous eigenvalue branch. Furthermore, the differential expressions of the eigenvalues with respect to each of parameters are given.

Keywords

fourth-order differential operatoreigenparameter-dependent boundary conditiondependence of eigenvaluedifferential expression
CLC number: 34B05, 34L30, 47E05

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9247-9260
DOI: 10.3934/math.2022512

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Cite this article:
Qin J, Li K, Zheng Z, et al. Eigenvalues of fourth-order differential operators with eigenparameter dependent boundary conditions. AIMS Mathematics, 2022, 7(5): 9247-9260. https://doi.org/10.3934/math.2022512

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Received: 25 November 2021
Revised: 13 February 2022
Accepted: 22 February 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)