On a Class of Degenerate Nonlinear Elliptic Equations in Weighted Sobolev Spaces

In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate nonlinear elliptic equations\[ {aligned} & -∑ⱼ₌₁ⁿ D_j [ ω(x) B_j(x, u, ∇ u) ] - ∑i,j=1ⁿ D_j ( aᵢⱼ(x) D_i u(x) ) + b(x, u, ∇ u)\, ω(x) + g(x)\, u(x) \\ & = f_0(x) - ∑ⱼ₌₁ⁿ D_j f_j(x), in Ω {aligned} \]in the setting of the weighted Sobolev spaces W1,p_ 0 (Ω,ω).