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Topological methods for an elliptic equation with exponential nonlinearities
We consider a class of variational
equations with exponential nonlinearities 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
equation. This is used together with a min-max argument to obtain
existence results.