IUMJ

Title: Symmetry results for cooperative elliptic systems in unbounded domains

Authors: Lucio Damascelli, Filomena Pacella and Francesca Gladiali

Issue: Volume 63 (2014), Issue 3, 615-649

Abstract:

In this paper, we prove symmetry results for classical solutions of semilinear cooperative elliptic systems in $\mathbb{R}^N$, $N\geq2$, 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.