Groundstates for nonlinear fractional Choquard equations with general nonlinearities

Abstract

We study the following nonlinear Choquard equation driven by a fractional Laplacian: $$(-\Delta {)}^{s}u+u=(|x{|}^{-\mu }\ast F(u))f(u)|4.14mmin|1.14mm{\mathbb{R}}^N,$$ with $N\ge 3$, $s\in (0,1)$ and $\mu \in (0,N)$. 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.

There is a serious mistake in the proof that we can not cover the gap at this moment

References in corpus (1)

• On fractional Choquard equations

Cited by in corpus (1)

• Existence of solutions for a class of nonlinear Choquard equations with critical growth