# American Institute of Mathematical Sciences

December  2015, 35(12): 5869-5877. doi: 10.3934/dcds.2015.35.5869

## Symmetry of components, Liouville-type theorems and classification results for some nonlinear elliptic systems

 1 LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens

Received  December 2013 Published  May 2015

We prove the symmetry of components and some Liouville-type theorems for, possibly sign changing, entire distributional solutions to a family of nonlinear elliptic systems encompassing models arising in Bose-Einstein condensation and in nonlinear optics. For these models we also provide precise classification results for non-negative solutions. The sharpness of our results is also discussed.
Citation: Alberto Farina. Symmetry of components, Liouville-type theorems and classification results for some nonlinear elliptic systems. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5869-5877. doi: 10.3934/dcds.2015.35.5869
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##### References:
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