Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Address: Department of Mathematics, State University of Londrina, Londrina - PR - Brazil, 86057-970

E-mail: accava@gmail.com

Abstract: In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with 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) {\mathcal{A}}_j(x, u, {\nabla }u){\bigr ]}\\ =&\ f_0(x) - \sum _{j=1}^nD_jf_j(x)\,, \quad \mbox {in}\quad {\Omega } in the setting of the weighted Sobolev spaces.

AMSclassification: primary 35J70; secondary 35J60.

Keywords: degenerate nonlinear elliptic equations, weighted Sobolev spaces.

DOI: 10.5817/AM2014-1-51