Multiplicity of solutions for an elliptic equation with exponential growth

Abstract

We prove existence of two solutions for an elliptic equation with exponential growth on a bounded domain. The first solution is obtained by an approximation scheme together with a fixed point theorem. The second solution is found by variational methods, and its expression is given by the sum of the first solution by other adequate function. The nonlinearities may have subcritical, critical or supercritical exponential growth.