Electron. J. Differential Equations, Vol. 2020 (2020), No. 105, pp. 1-15.

Nonlinear degenerate elliptic equations in weighted Sobolev spaces

Aharrouch Benali, Bennouna Jaouad

Abstract:
We study the existence of solutions for the nonlinear degenerated elliptic problem

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.
DOI: 10.58997/ejde.2020.105

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Aharrouch Benali
Sidi Mohamed Ben Abdellah University
Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
P.O. Box 1796 Atlas Fez, Morocco
email: bnaliaharrouch@gmail.com
Bennouna Jaouad
Sidi Mohamed Ben Abdellah University
Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
P.O. Box 1796 Atlas Fez, Morocco
email: jbennouna@hotmail.com

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