Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane

We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equations -Delta u + u=(I-alpha* F(u))F'(u) in R-2, where I-alpha is the Riesz potential of order alpha on the plane R-2 under general nontriviality, growth and subcriticality on the nonlinearity F is an element of C-1 (R, R).