Remark for Certain Elliptic PDE with Exponential Nonlinearity in a Bounded Domain

In this note, we are concerned with a class of semi-linear elliptic pdes with exponential nonlinearity in a bounded domain. Here, the nonlinearity is more or less growing exponentially with power p. We consider the problem under two types of Dirichlet boundary condition. We give existence and non-existence of solutions for those problems and some asymptotics.