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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 243740, 15 pages
http://dx.doi.org/10.1155/2012/243740
Research Article

A New Solution Operator of One-Dimensional -Laplacian with a Sign-Changing Weight and Its Application

1Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea
2Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea

Received 22 February 2012; Accepted 7 May 2012

Academic Editor: Ferhan M. Atici

Copyright © 2012 Inbo Sim and Yong Hoon Lee. 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 establish a new solution operator for the following problem , , , where , . may be singular at the boundary or change signs or may not be in so that this solution operator can cover larger class of than previously known ones. As an application, by checking complete continuity of the solution operator, we show the existence of nontrivial solutions for -Laplacian , , , where a parameter and and and may change signs or may be beyond of .