Abstract and Applied Analysis
Volume 2010 (2010), Article ID 658397, 21 pages
doi:10.1155/2010/658397
Research Article

Multiple Positive Solutions for Semilinear Elliptic Equations in ℝN Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

Tsing-San Hsu and Huei-Li Lin

Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan

Received 1 November 2009; Revised 19 March 2010; Accepted 9 June 2010

Academic Editor: Norimichi Hirano

Copyright © 2010 Tsing-San Hsu and Huei-Li Lin. 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 study the existence and multiplicity of positive solutions for the following semilinear elliptic equation -Δu+u=λa(x)|u|q-2u+b(x)|u|p-2u in ℝN, u∈H1(ℝN), where λ>0, 1<q<2<p<2* (2*=2N/(N-2) if N≥3, 2*=∞ if N=1,2), a(x), b(x) satisfy suitable conditions, and a(x) may change sign in ℝN.