Existence and Uniqueness of Solutions for the Navier Problems with Degenerate Nonlinear Elliptic Equations

Abstract

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations ${\Delta}(v(x)\, {\vert{\Delta}u\vert}^{p-2}{\Delta}u) -\sum_{j=1}^n D_j{\bigl[}{\omega}(x) {\cal A}_j(x, u, {\nabla}u){\bigr]}+ b(x,u,{\nabla}u)\, {\omega}(x) = f_0(x) -\sum_{j=1}^nD_jf_j(x), \ \ {\rm in } \ \ {\Omega}$ in the setting of the Weighted Sobolev Spaces