Existence of groundstates for a class of nonlinear Choquard equations in the plane

Luca Battaglia, Jean Van Schaftingen

We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$-\Delta u+u=(I_{\alpha }\ast F(u))F^{\prime }(u)\text{in }{\mathbb{R}}^2,$$ where $I_{\alpha }$ is the…