Groundstates for nonlinear fractional Choquard equations with general nonlinearities

We study the following nonlinear Choquard equation driven by a fractional Laplacian: $(-Δ)^{s}u+ u =(|x|^{-μ}\ast F(u))f(u)|{4.14mm}{in}|{1.14mm} \mathbb{R}^N,$ with $N\geq3$, $s\in(0,1)$ and $μ\in(0,N)$. By Supposing that the nonlinearities satisfy the general Berestycki-Lions type conditions \cite{BL}, we are able to prove the existence of groundstates for this equation by variational methods.

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