Existence results for some nonlinear elliptic equations via topological degree methods

This article is devoted to study the existence of weak solutions to a Dirichlet boundary value problem related to the following nonlinear elliptic equation -div(a(x,u, del u) - lambda g(x, u, del u) = b(x)vertical bar u vertical bar(q-2)u, where -div(a(x,u, del u) is a Leray-Lions operator acting from W-0(1,p)(Omega, w) to its dual W--1,W-p '(Omega, w*). On the nonlinear term g(x, s, eta), we only assume the growth condition on eta. Our approach is based on the topological degree introduced by Berkovits.