On a Class of Anisotropic Elliptic Equations with Hardy Potential and Homogeneous Neumann Boundary Conditions

Ayoub EL HAFIANE; Abderrazak   Kassidi; Ali  El Mfadel; Mhamed  Elomari

doi:10.5269/bspm.77819

On a Class of Anisotropic Elliptic Equations with Hardy Potential and Homogeneous Neumann Boundary Conditions

On a Class of Anisotropic Elliptic Equations

Ayoub EL HAFIANE Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
Abderrazak Kassidi Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
Ali El Mfadel Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
Mhamed Elomari Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

DOI: https://doi.org/10.5269/bspm.77819

Résumé

We study a class of anisotropic nonlinear elliptic problems involving a Hardy potential and subject to homogeneous Neumann boundary conditions. The differential operator under consideration is of the Leray-Lions anisotropic type. By employing Berkovits' topological degree theory, combined with the properties of anisotropic Sobolev spaces and the abstract Hammerstein equation, we establish the existence of weak solutions to the problem under investigation.