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 ∈ πi=1 nlp' (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 g(x,s,ξ) sgn(s) ≥ ρ∑i=1 n ωi|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. © 2015 lili dai et al.