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

We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu − μ/|x|2u λfx|u|q−2u gx|u|2∗−2u in Ω, u 0 on ∂Ω, where 0 ∈ Ω ⊂ RNN ≥ 3 is a bounded domain with smooth boundary ∂Ω, λ> 0, 0 ≤ μ < μ N − 22/4, 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. Copyright q 2009 T.-S. Hsu and H.-L. 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