Existence of Solutions for Degenerate Elliptic Problems in Weighted Sobolev Space

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