# Groundstate solutions for a nonlinear Choquard equation

##
Luca Battaglia

created by malchiodi on 13 Nov 2016

17 nov 2016
-- 17:00
[open in google calendar]

Scuola Normale Superiore, Aula Tonelli

**Abstract.**

I will discuss the existence of groundstate solutions for the Choquard equation in the whole space R^{N.
}
I will first consider the case of a homogeneous nonlinearity F(u)=

u

^{p,} then I will prove the existence of solutions under general hypotheses. In particular, the cases N = 2 and N >= 3 will have to be treated differently.
The solutions are found through a variational mountain pass strategy.