Some existence results for a class of Dirichlet problems with variable exponents

In this paper, we study the existence and multiplicity of weak solutions of the p(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p(x)$\end{document}-Laplacian problems that are subject to Dirichlet boundary conditions, employing variational techniques as our primary analytical framework.