Multiple solutions for a class of quasilinear elliptic problems with discontinuous nonlinearities and weights

Abstract

In this paper, using nonsmooth critical point theory, we study the existence of multiple solutions of the following class of problems: {−div(|x|−ap|∇u|p−2∇u)∈λ|x|−(a+1)p+c[f−(u),f+(u)],x∈Ω,u=0,x∈∂Ω, where a,c,λandf−,f+ satisfy certain conditions.