Seminar Analysis: Luca Battaglia (University of Rome, La Sapienza)

Groundstate solutions for a nonlinear Choquard equation

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.

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