Boundary Value Problems
Volume 2009 (2009), Article ID 532546, 7 pages
doi:10.1155/2009/532546
Research Article

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

Chen Yu and Li Yongqing

School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou 350007, China

Received 23 March 2009; Accepted 10 June 2009

Academic Editor: Martin Schechter

Copyright © 2009 Chen Yu and Li Yongqing. 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 consider a similinear elliptic equation with sign-changing potential −Δu−V(x)u=f(x,u), u∈H1(ℝN), where V(x) is a function possibly changing sign in ℝN. Under certain assumptions on f, we prove that the equation has infinitely many solutions.