The Singular Perturbation Of A Class Of Singular Elliptic Problem

In this paper,we consider the existence and multiplicity of solutions for the following nonlinear singular elliptic problem where Ω is a bounded smooth domain in RN(N≥3),λ>0,λ>0 are real parameters,β> 2*-1,γ>0 are constants,a(x)≥0 is a nontrivial measurable function which may be unbounded,f is a Caratheodory function.We treat the problem in H01(Ω)∩L∞ (Ω).To overcome the difficulty caused by the supercritical term uβ,we truncate the problem into the subcritical problem.By weak super-subsolution method and the mountain pass lem-ma, we find the truncated problem has two weak solutions,and by the Moser iteration, we prove that the solutions of the truncated problem are just the solutions of the original problem withλ and μ small enough.