Anisotropic Nonlinear Elliptic Equations with Variable Exponents and Two Weighted First Order Terms

Abstract

This paper is devoted to studying the existence of distributional solutions for a boundary value problems associated to a class of anisotropic nonlinear elliptic equations with variable exponents characterized by two strictly positive$-\mathring{W}^{1,\overrightarrow{p}(\cdot)}(\Omega)$ first order terms (the weight functions belong to the anisotropicvariable exponents Sobolev space with zero boundary), and this is in bounded open Lipschitz domain (with Lipschitz boundary) of $\mathbb{R}^N$ ($N\ge 2$). The functional setting involves anisotropic varible exponents Lebesgue-Sobolev spaces.