Abstract and Applied Analysis
Volume 2011 (2011), Article ID 828176, 16 pages
http://dx.doi.org/10.1155/2011/828176
Research Article

The Eigenfunction Expansion for a Dirichlet Problem with Explosive Factor

Zaki F. A. El-Raheem1 and A. H. Nasser2

1Department of Mathematics, Faculty of Education, Alexandria University, Alexanderia 21526, Egypt
2Department of Mathematics, Faculty of Industrial Education, Helwan University, Cairo, Egypt

Received 10 February 2011; Accepted 2 May 2011

Academic Editor: Pavel Drábek

Copyright © 2011 Zaki F. A. El-Raheem and A. H. Nasser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the eigenfunction expansion formula for a Dirichlet problem with explosive factor by two ways, first by standard method and second by proving a convergence in some metric space 𝐿 2 ( 0 , 𝜋 ; 𝜌 ( 𝑥 ) ) .