Eigenvalue properties of Sturm-Liouville problems with transmission conditions dependent on the eigenparameter

Autor:	Lanfang Zhang, Jijun Ao, Na Zhang
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	sturm-liouville problems eigenparameter-dependent transmission conditions green's function dependence of eigenvalues Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 32, Iss 3, Pp 1844-1863 (2024)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2024084?viewType=HTML
Popis:	This paper studies a discontinuous Sturm-Liouville problem in which the spectral parameter appears not only in the differential equation but also in the transmission conditions. By constructing an appropriate Hilbert space and inner product, the eigenvalue and eigenfunction problems of the Sturm-Liouville problem are transformed into an eigenvalue problem of a certain self-adjoint operator. Next, the eigenfunctions of the problem and some properties of the eigenvalues are given via construction of the basic solution. The Green's function for the Sturm-Liouville problem is also given. Finally, the continuity of the eigenvalues and eigenfunctions of the problem is discussed. Especially, the differential expressions of the eigenvalues for some parameters have been obtained, including the parameters in the eigenparameter-dependent transmission conditions.
Databáze:	Directory of Open Access Journals
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