Existence of Solutions for Degenerate Elliptic Problems in Weighted Sobolev Space

Abstract

This paper is devoted to the study of the existence of solutions to a general elliptic problemAu+g(x,u,∇u)=f-div⁡F, withf∈L1(Ω)andF∈∏i=1NLp'(Ω,ωi*), whereAis a Leray-Lions operator from a weighted Sobolev space into its dual andg(x,s,ξ)is a nonlinear term satisfyinggx,s,ξsgn⁡(s)≥ρ∑i=1Nωi|ξi|p,|s|≥h>0, and a growth condition with respect toξ. Here,ωi,ωi*are weight functions that will be defined in the Preliminaries.