Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 105, pp. 1-15.

Title: Nonlinear degenerate elliptic equations in weighted Sobolev spaces
       
Authors: Aharrouch Benali (Sidi Mohamed Ben Abdellah Univ., Fez, Morocco)
         Bennouna Jaouad  (Sidi Mohamed Ben Abdellah Univ., Fez, Morocco)

Abstract:
 We study the existence  of solutions for the nonlinear degenerated elliptic problem
 $$\displaylines{ 
 -\operatorname{div} a(x,u,\nabla u)=f \quad\text{in } \Omega,\cr
 u=0 \quad\text{on }\partial\Omega,
 }$$
 where $\Omega$ is a bounded open set in $\mathbb{R}^N$, $N\geq2$, a is a Caratheodory
 function  having degenerate coercivity 
 $a(x,u,\nabla u)\nabla u\geq \nu(x)b(|u|)|\nabla u|^p$,
 1<p<N,  $\nu(\cdot)$ is the weight function, 
 b is continuous and $f\in L^r(\Omega)$.
 
Submitted December 4, 2019. Published October 12, 2020.
Math Subject Classifications: 35J70, 46E30, 35J85.
Key Words: Nonlinear degenerated elliptic operators;  weighted Sobolev space;
           monotony and rearrangement methods.