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Symmetry of components for semilinear elliptic systems

Thursday, September 27, 2012 - 11:30am - 12:20pm
Keller 3-180
Pavol Quittner (Comenius University in Bratislava)
We give sufficient conditions ensuring that any positive classical solution (u,v) of an elliptic system in the whole n-dimensional space has the symmetry property u=v. As an application, we improve some known results on Sobolev-critical elliptic systems of Schrodinger type. Our techniques apply to some supercritical problems as well. We also obtain new Liouville-type theorems for non-cooperative systems. Moreover, we provide several counterexamples which indicate that our assumptions are in a sense necessary.

This is a joint work with Philippe Souplet.
MSC Code: 
35J61