existence and uniqueness of weak solution in weighted sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data

In this paper, we study the existence and uniqueness of weak solution to a dirichlet boundary value problems for the following nonlinear degenerate elliptic problems −divh ω1a(x, ∇u) + ν2b(x, u, ∇u) i + ν1c(x, u) + ω2|u| p−2u = f − divf, where 1 < p < ∞, ω1, ν2, ν1 and ω2 are ap-weight functions, and a : ω × rn → rn, b : ω × r × rn → rn , c : ω × r → r are caratéodory functions that satisfy some conditions and the right-hand side term f − divf belongs to l p´(ω, ω 1−p´2 ) + ∏n j=1 l p´ (ω, ω 1−p´ 1). we will use the browder minty theorem and the weighted sobolev spaces theory to prove the existence and uniqueness of weak solution in the weighted sobolev space w 1,p 0 (ω, ω1, ω2).