The Modified Parseval Equality of Sturm-Liouville Problems with Transmission Conditions

Mudan Bai, Jiong Sun and Siqin Yao

Journal of Applied Mathematics, 2013, vol. 2013, 1-11

Abstract:

We consider the Sturm-Liouville (S-L) problems with very general transmission conditions on a finite interval. Firstly, we obtain the sufficient and necessary condition for being an eigenvalue of the S-L problems by constructing the fundamental solutions of the problems and prove that the eigenvalues of the S-L problems are bounded below and are countably infinite. Furthermore, the asymptotic formulas of the eigenvalues and eigenfunctions of the S-L problems are obtained. Finally, we derive the eigenfunction expansion for Green's function of the S-L problems with transmission conditions and establish the modified Parseval equality in the associated Hilbert space.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:619358

DOI: 10.1155/2013/619358

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