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Elliptic Systems with Nonlinearities of Arbitrary Growth

Authors:	Email author" target="_blank">Djairo?G?de?Figueiredo Email author Bernhard?Ruf

Institution:	(1) IMECC, Universidade Estadual de Campinas, 13081-970 Campinas, SP, Brazil;(2) Dipartimento di Matematica, Università degli Studi, Via Saldini 50, 20133 Milano, Italy

Abstract:	In this paper we study the existence of nontrivial solutions for the following system of coupled semilinear Poisson equations: $\left\{ {\begin{array}{*{20}l} { - \Delta u = v^p ,} & {{\text{in }}\Omega ,} \\ { - \Delta v = f(u),} & {{\text{in }}\Omega ,} \\ {u = 0{\text{ and }}v = 0,} & {{\text{on }}\partial \Omega ,} \\ \end{array} } \right.$ where is a bounded domain in $\mathbb{R}^N .$ We assume that $0 < p < \frac{2} {{N - 2}},$ and the function f is superlinear and with no growth restriction (for example f(s) = s e^s); then the system has a nontrivial (strong) solution.

Keywords:	35J50 35J55
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