On a class of nonhomogeneous anisotropic elliptic problem with variable exponents

In this investigation, we study the existence of weak solution for a class of nonhomogeneous anisotropic elliptic problem. These problems involve the anisotropic operators with variable exponents. Based on the topological degree theory concerning a specific subset of demicontinuous operators under generalized (S+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(S_+)$$\end{document} and the theory of anisotropic Sobolev spaces with variable exponent, we demonstrate the existence of weak solution for this problem. Our findings are applicable to problems with no-flux boundary conditions, and they extend and generalize several results previously reported in the literature.