Title: Ground state solutions for a nonlinear Choquard equation,
Abstract: We discuss the existence of ground state solutions for the Choquard equation
$$-\Delta u=(I_\alpha*F(u))F'(u)\quad\quad\quad\text{in }\mathbb R^N.$$ We
prove the existence of solutions under general hypotheses, investigating in
particular the case of a homogeneous nonlinearity $F(u)=\frac{|u|^p}p$. The
cases $N=2$ and $N\ge3$ are treated differently in some steps. The solutions
are found through a variational mountain pass strategy. The result presented
are contained in the papers with arXiv ID 1212.2027 and 1604.03294