Anisotropic obstacle Neumann problems in weighted Sobolev spaces with Hardy potential and variable exponent

In this paper, we focus on a class of anisotropic obstacle problems governed by a Leray-Lions operator, involving non-linear elliptic equations with a Hardy potential exhibiting variable growth. Additionally, these problems are equipped by homogeneous Neumann boundary conditions. Using truncation techniques and the monotonicity method, we establish the existence of entropy solutions for the studied problem within the framework of anisotropic weighted Sobolev spaces with a variable exponent. © The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada 2024.