Existence of Solutions to Elliptic Equation with Exponential Nonlinearities and Singular Term

Abstract

In this paper, we consider an elliptic equation with exponential nonlinearities and singular term. By constructing the corresponding variational framework, and using a Singular Trudinger-Moser inequality due to Li, Mountain-pass theorem and the Ekeland’s variational principle, we get a nontrivial positive weak solution.