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arXiv · 1412.3184

Groundstates for nonlinear fractional Choquard equations with general nonlinearities

Zifei Shen·Fashun Gao·Minbo Yang
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Abstract

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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Zifei Shen, Fashun Gao, Minbo Yang. 2015-01-07. Groundstates for nonlinear fractional Choquard equations with general nonlinearities. https://arxiv.org/abs/1412.3184

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