Calculus of Variations and Geometric Measure Theory
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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 RN. 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.

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