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 - d i v a ( x , u , ∇ u ) - λ g ( x , u , ∇ u ) = b ( x ) | u | q - 2 u , where - d i v a ( x , u , ∇ u ) is a Leray-Lions operator acting from W 0 1 , p ( Ω , w ) to its dual W - 1 , p ′ ( Ω , w ∗ ) . On the nonlinear term g ( x , s , η ) , we only assume the growth condition on η . Our approach is based on the topological degree introduced by Berkovits.