The Positive Solutions Of A Class Of Singular Elliptic Problem

In this paper, we consider the existence and multiplicity of positive solutions for nonlinear singular elliptic problems: where Q is a bounded C2 domain in RN, N≥3, γ> 0,μ> 0, β> 2* - 1(2*= 2N/N-2) are constants, λ> 0 is a parameter, α≥ 0 is a nontrivial measurable function and there is cpo ∈ C10(0.) and q> n such that a(x)(?)0 ∈ Lq(Ω), f is a Caratheodory function satisfying some certain conditions. Then the singular ellip-tic problem (P) has two weak solutions with small λ. Since the energy functional of supercritical growth has no longer compactness, we can solve the subcriti-cal problem by truncating the supercritical problem. Finally through the Moser iteration, we prove that the solutions of the truncated problem are just the solu-tions of the original nonlinear singular elliptic problem. During the process, the first weak solution is mainly obtained by the method of truncating the upper and lower solutions, while the second one is mainly obtained by mountain pass lemma.