Existence of Solutions for Degenerate Elliptic Problems in Weighted Sobolev Space

Abstract EN

This paper is devoted to the study of the existence of solutions to a general elliptic problem A u + g ( x , u , ∇ u ) = f - div F , with f ∈ L 1 ( Ω ) and F ∈ ∏ i = 1 N L p ' ( Ω , ω i * ) , 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 ω i | ξ i | p , | s | ≥ h > 0 , and a growth condition with respect to ξ .

Here, ω i , ω i * are weight functions that will be defined in the Preliminaries.