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, issue 1

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 λ 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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https://doi.org/10.1155/2013/619358

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:619358

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