# FRB

## Seminar

### Existence and Qualitative Properties of Grounds States to the Choquard-Type Equations

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Co-author: Jean Van Schaftingen (Louvain-la-Neuve, Belgium)The Choquard equation, also known as the Hartree equation or nonlinear Schrodinger-Newton equation is a stationary nonlinear Schrodinger type equation 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 equations in exterior domains and consider existence, positivity, symmetry and optimal decay properties of ground state solutions under various assumptions on the decay of the external potential and the shape of the nonlinearity. We also discuss the existence of semiclassical solutions to the equation.

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