Topological methods for an elliptic equation with exponential nonlinearities

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January 2008, 21(1): 277-294. doi: 10.3934/dcds.2008.21.277

Topological methods for an elliptic equation with exponential nonlinearities

1.	SISSA, via Beirut 2-4, 34014 Trieste

Received December 2006 Revised October 2007 Published February 2008

Abstract
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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.

Keywords: variational methods, min-max schemes., Geometric PDEs.

Mathematics Subject Classification: 35B33, 35J35, 53A30, 53C2.

Citation: Andrea Malchiodi. Topological methods for an elliptic equation with exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 277-294. doi: 10.3934/dcds.2008.21.277

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