For EDITORS

For READERS

All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Semiclassical solutions of the Choquard equations in $\mathbb{R}^{3}$
fei Zi Shen,Ke Jin
Keywords:Choquard equations; Semiclassical States; Lyapunov--Schmidt reduction
Abstract:
      We study the nonlocal equation: $$ -\varepsilon^{2}\Delta u+\lambda u+V(x)u=\varepsilon^{-2}(|x|^{-1}*|u|^{p})|u|^{p-2}u\hspace{10.64mm} \mbox{in}\hspace{1.14mm} \mathbb{R}^{3}, $$ where $\varepsilon>0$ is a small parameter, $\lambda>0$, $0<p<\infty$ are positive constants and $u$ is a real-valued measurable function. By Lyapunov--Schmidt reduction, we will prove the existence of multiple semiclassical solutions.