Research Article

Eigenvalues of Sturm-Liouville problems with distributional potentials and eigenparameter-dependent boundary conditions

Published in: Quaestiones Mathematicae
Volume 46 , issue 3 , 2023 , pages: 445–464

DOI: 10.2989/16073606.2022.2033337

Author(s): Ji-Jun Ao Inner Mongolia University of Technology, China , Meng-Lei Li Inner Mongolia University of Technology, China , Hai-Yan Zhang Inner Mongolia University of Technology, China

Keywords: Primary: 34L10 , 34B20 , Secondary: 47A45 , Sturm-Liouville problems , distributional potentials , eigenparameter-dependent boundary conditions , eigenvalues

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Abstract

In this paper, regular Sturm-Liouville problems with distributional potentials and eigenparameter-dependent boundary conditions are investigated. We obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problem: the coeﬃcients, the boundary conditions, and the endpoints, in particular, the eigenparameter-dependent boundary condition matrix. Moreover, we find the diﬀerential expressions for each parameters.

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