Nonlinear Elliptic Equations With Variable Exponents Involving Singular Nonlinearity

TL;DR

This paper establishes existence and regularity of positive solutions for nonlinear elliptic equations with singular nonlinearities and variable exponents, highlighting the regularizing effect of lower order terms in variable exponent Sobolev spaces.

Contribution

It generalizes previous results by proving existence and regularity for equations with singular nonlinearities in variable exponent Sobolev spaces, including the regularizing influence of lower order terms.

Findings

Existence of weak positive solutions is proven.

Lower order terms have a regularizing effect.

Results extend previous work to variable exponent settings.

Abstract

In this paper, we prove the existence and regularity of weak positive solutions for a class of nonlinear elliptic equations with a singular nonlinearity, lower order terms and $L^{1}$ datum in the setting of variable exponent Sobolev spaces. We will prove that the lower order term has some regularizing effects on the solutions. This work generalizes some results given in \cite{1}.