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

Multiple positive solutions for singular elliptic equations with concave-convex nonlinearities and sign-changing weights

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.