English

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 s(12,1)s\in(\frac{1}{2}, 1), (y,y)R2×RN2(y',y'')\in \mathbb{R}^2\times \mathbb{R}^{N-2}, V(y,y)V(|y'|,y'') 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.

Keywords

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}
}
R2 v1 2026-06-23T08:42:50.474Z