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Topological methods for an elliptic equation with exponential nonlinearities

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  • 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.
    Mathematics Subject Classification: 35B33, 35J35, 53A30, 53C21.


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