Multiple positive solutions for p-Laplace elliptic equations involving concaveconvex nonlinearities and a Hardy-type term

摘要

In this paper, the following problem is considered: -Δpu-μ|u|p- 2u|x|p=λf(x)|u|q-2u+g(x)|u|p*-2u,x∈Ω,u=0, x∈?Ω, where Ω?RN is a bounded domain such that 0∈Ω, 10, μ<μ,f and g are nonnegative functions, μ=(N-pp)p is the best Hardy constant and p*=NpN-p is the critical Sobolev exponent. By extracting the PalaisSmale sequence in the Nehari manifold, the existence of multiple positive solutions to this equation is verified.