Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces

In this paper, we prove the existence and uniqueness of solution to a Dirichlet boundary value problems for the following nonlinear degenerate elliptic equation - div [ ω 1 A ( x , ∇ u ) + ω 2 B ( x , u , ∇ u ) ] + ω 3 b ( x , u ) + ω 4 | u | p - 2 u = f ( x ) , where ω 1 , ω 2 , ω 3 and ω 4 are weight functions, A : Ω × R n ⟶ R n , B : Ω × R × R n ⟶ R n , b : Ω × R ⟶ R are Caratéodory functions that satisfy some conditions and the right-hand side term f belongs to L 1 ( Ω ) .