Existence of solutions for an elliptic problem with degenerate coercivity.

Abstract

We study the existence of solutions for the following problem $$\left\{\begin{array}{lll} A(u)+H(x,u,\nabla u)=f &\mbox{in}& \Omega,\\ u=0 &\mbox{on} &\partial\Omega, \end{array}\right.$$ where, $A$ is a Loray-Lions operator from $W_0^{1,p}(\Omega, \nu)$ into its dual, while $H(x,s,\xi)$ is a nonlinear term witch has a growth condition with respect to $\xi$. For the right hand side $f$, we will make a different assumptions.