On some nonlinear elliptic problems in anisotropic Orlicz–Sobolev spaces

In this study, the Dirichlet problem for a particular class of anisotropic elliptic equations is taken into account. The right-hand side of these equations is framed in anisotropic Orlicz–Sobolev spaces, and it is described by an Orlicz function that does not meet the Δ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta 2$$\end{document}-condition. Within this framework of these spaces, the existence and uniqueness of the weak solution are established.