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.
Citation
Mudan Bai. Jiong Sun. Siqin Yao. "The Modified Parseval Equality of Sturm-Liouville Problems with Transmission Conditions." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/619358