Boundary Value Problems
Volume 2009 (2009), Article ID 584203, 17 pages
doi:10.1155/2009/584203
Research Article

Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights

Tsing-San Hsu and Huei-Li Lin

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

Received 5 December 2008; Accepted 11 March 2009

Academic Editor: Pavel Drabek

Copyright © 2009 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 existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu−(μ/|x|2)u=λf(x)|u|q−2u+g(x)|u|2∗−2u in Ω, u=0 on ∂Ω, where 0∈Ω⊂ℝN(N≥3) is a bounded domain with smooth boundary ∂Ω, λ>0, 0≤μ<μ¯=(N−2)2/4, 2∗=2N/(N−2), 1≤q<2, and f, g are continuous functions on Ω¯ which are somewhere positive but which may change sign on Ω.