Symmetry results for cooperative elliptic systems in unbounded domains
Lucio DamascelliFrancesca GladialiF. Pacella
35B0635B5035J4735G60Cooperative elliptic systemsSymmetryMaximum PrincipleMorse index
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.
Indiana University Mathematics Journal
2014
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10.1512/iumj.2014.63.5255
10.1512/iumj.2014.63.5255
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Indiana Univ. Math. J. 63 (2014) 615 - 649
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