Nonlinear Elliptic Equations With Variable Exponents Involving Singular Nonlinearity

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 [2].