Existence of a semilinear elliptic system with exponential nonlinearities
Dongho Chae · Discrete and Continuous Dynamical Systems · 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.