Solutions for fractional operator problem via local Pohozaev identities
Analysis of PDEs
2019-04-18 v1
Abstract
We consider the following fractional Schr\"{o}dinger equation involving critical exponent: \begin{equation*} \left\{\begin{array}{ll} (-\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \ \hbox{ in } \ \mathbb{R}^N, \\ u>0, \ y \in \mathbb{R}^N, \end{array}\right. \end{equation*} where , , is a bounded nonnegative function with a weaker symmetry condition. We prove the existence of infinitely many solutions for the above problem by a finite dimensional reduction method combining various Pohazaev identies.
Cite
@article{arxiv.1904.08316,
title = {Solutions for fractional operator problem via local Pohozaev identities},
author = {Yuxia Guo and Ting Liu and Jianjun Nie},
journal= {arXiv preprint arXiv:1904.08316},
year = {2019}
}