EconPapers    
Economics at your fingertips  
 

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
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/619358

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

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

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().

 
Page updated 2025-04-24
Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:619358