Existence, nonexistence and optimal decay of solutions to nonlinear Choquard equations
Thursday 14 February 2013
2:00 pm - 3:00 pm
2:00 pm - 3:00 pm
| Event type | Seminar |
| Location | John Crank - Room 128 |
Speaker: Vitaly Moroz, Swansea University
Abstract
Choquard (aka nonlinear Schrodinger-Newton or Hartree) equation is a stationary nonlinear Schrodinger type equation where the nonlinearity is coupled with a nonlocal convolution term (gravitational potential).
We present sharp Liouville-type theorems on nonexistence of positive supersolutions of such equations in exterior domains. We also discuss existence and optimal decay properties of positive solutions under various assumptions on the decay of the external potential and "nearly" optimal conditions on the nonlinearity which ensure the existence of a ground state solution to the equation.
This is joint work with Jean Van Schaftingen (Louvain-la-Neuve, Belgium).
