Nonlinear degenerate elliptic equations in weighted Sobolev spaces

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 \(f\in L^r(\Omega)\). For more information see https://ejde.math.txstate.edu/Volumes/2020/105/abstr.html