Dependence of eigenvalues for higher odd-order boundary value problems

Antong Ji and Meizhen Xu

Applied Mathematics and Computation, 2024, vol. 467, issue C

Abstract: This paper is concerned with higher odd-order boundary value problems. We first prove that the operators associated with the problems are symmetric and the corresponding eigenvalues are real, and we give the resolvent operators related to the differential operators. Then we obtain that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem. Moreover, the differential expressions of the eigenvalues as regards these parameters are given. In particular, we give the Frechet derivatives of the eigenvalues for the leading coefficient function q0 and coefficient functions q1,⋯,qn.

Keywords: Odd-order differential operator; Boundary value problems; Dependence of eigenvalues; Differential expression (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:467:y:2024:i:c:s0096300323006562

DOI: 10.1016/j.amc.2023.128487

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