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Existence of a semilinear elliptic system with exponential nonlinearities

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  • 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.
    Mathematics Subject Classification: Primary: 35J60, 35J65; Secondary: 35Q80.


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