Journal of Applied Mathematics

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

Mudan Bai, Jiong Sun, and Siqin Yao

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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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 619358, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808207

Digital Object Identifier
doi:10.1155/2013/619358

Mathematical Reviews number (MathSciNet)
MR3127464

Zentralblatt MATH identifier
06950781

Citation

Bai, Mudan; Sun, Jiong; Yao, Siqin. The Modified Parseval Equality of Sturm-Liouville Problems with Transmission Conditions. J. Appl. Math. 2013 (2013), Article ID 619358, 11 pages. doi:10.1155/2013/619358. https://projecteuclid.org/euclid.jam/1394808207


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