Topological methods for an elliptic equation with exponential nonlinearities

We consider a class of variational equations with exponential non- linearities on compact surfaces. From considerations involving the Moser- Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equa- tion. This is used together with a min-max argument to obtain existence results.