# American Institute of Mathematical Sciences

November  2007, 18(4): 709-718. doi: 10.3934/dcds.2007.18.709

## Existence of a semilinear elliptic system with exponential nonlinearities

 1 Department of mathematics, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, 440-746, South Korea

Received  June 2006 Revised  February 2007 Published  May 2007

We consider a system of semilinear elliptic partial differential equations with exponential nonlinearities in $R^2$. We construct a solution of the system viewing the system as a perturbation of the decoupled Liouville equations and applying suitable implicit function theorem. As a byproduct we obtain very precise information on the asymptotic behaviors of the solutions near infinity.
Citation: Dongho Chae. Existence of a semilinear elliptic system with exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 709-718. doi: 10.3934/dcds.2007.18.709
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