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arXiv · 1212.4647

Symmetry results for cooperative elliptic systems in unbounded domains

Lucio Damascelli·Francesca Gladiali·Filomena Pacella
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Abstract

In this paper we prove symmetry results for classical solutions of semilinear cooperative elliptic systems in R^N, or in the exterior of a ball. We consider the case of fully coupled systems and nonlinearities which are either convex or have a convex derivative. The solutions are shown to be foliated Schwarz symmetric if a bound on their Morse index holds. As a consequence of the symmetry results we also obtain some nonexistence theorems.

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Lucio Damascelli, Francesca Gladiali, Filomena Pacella. 2012-12-19. Symmetry results for cooperative elliptic systems in unbounded domains. https://arxiv.org/abs/1212.4647

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