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SUMMARY:Existence and Qualitative Properties of Grounds States to the Choq
 uard-Type Equations - Moroz\, V (Swansea University)
DTSTART:20140626T103000Z
DTEND:20140626T110000Z
UID:TALK53177@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Jean Van Schaftingen (Louvain-la-Neuve\, Belgium) \
 n\nThe Choquard equation\, also known as the Hartree equation or nonlinear
  Schrodinger-Newton equation is a stationary nonlinear Schrodinger type eq
 uation where the nonlinearity is coupled with a nonlocal convolution term 
 given by an attractive gravitational potential. We present sharp Liouville
 -type theorems on nonexistence of positive supersolutions of such equation
 s in exterior domains and consider existence\, positivity\, symmetry and o
 ptimal decay properties of ground state solutions under various assumption
 s on the decay of the external potential and the shape of the nonlinearity
 . We also discuss the existence of semiclassical solutions to the equation
 .\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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