Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Existence of a semilinear elliptic system with exponential nonlinearities

Pages: 709 - 718, Volume 18, Issue 4, August 2007      doi:10.3934/dcds.2007.18.709

       Abstract        Full Text (154.9K)       Related Articles

Dongho Chae - Department of mathematics, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, 440-746, South Korea (email)

Abstract: 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.

Keywords:  exponential nonlinearity, existence, perturbation method.
Mathematics Subject Classification:  Primary: 35J60, 35J65; Secondary: 35Q80.

Received: June 2006;      Revised: February 2007;      Available Online: May 2007.