Open Access

Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential

Boundary Value Problems20092009:532546

DOI: 10.1155/2009/532546

Received: 23 March 2009

Accepted: 10 June 2009

Published: 16 June 2009

Abstract

We consider a similinear elliptic equation with sign-changing potential https://static-content.springer.com/image/art%3A10.1155%2F2009%2F532546/MediaObjects/13661_2009_Article_854_IEq1_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2009%2F532546/MediaObjects/13661_2009_Article_854_IEq2_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2009%2F532546/MediaObjects/13661_2009_Article_854_IEq3_HTML.gif is a function possibly changing sign in https://static-content.springer.com/image/art%3A10.1155%2F2009%2F532546/MediaObjects/13661_2009_Article_854_IEq4_HTML.gif . Under certain assumptions on https://static-content.springer.com/image/art%3A10.1155%2F2009%2F532546/MediaObjects/13661_2009_Article_854_IEq5_HTML.gif , we prove that the equation has infinitely many solutions.

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Authors’ Affiliations

(1)
School of Mathematics and Computer Sciences, Fujian Normal University

Copyright

© C. Yu and L. Yongqing. 2009

This article is published under license to BioMed Central Ltd. 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.