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

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  • 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.
    Mathematics Subject Classification: Primary: 35J50, 35B53; Secondary: 35J47.


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