Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations $$\begin{array}{rl}\mathrm{\Delta }(v(x){|\mathrm{\Delta }u|}^{p-2}\mathrm{\Delta }u)& -\sum _{j=1}^n{D}_j[{\omega }_1(x){\mathcal{A}}_j(x,u,\mathrm{\nabla }u)]+b(x,u,\mathrm{\nabla }u){\omega }_2(x)\\ & =f_0(x)-\sum _{j=1}^n{D}_j{f}_j(x),\mathrm{i}\mathrm{n}\mathrm{\Omega }\end{array}$$ in the setting of the weighted Sobolev spaces.