English

A Pohozaev Identity for the Fractional H$\acute{e}$non System

Analysis of PDEs 2017-08-11 v2

Abstract

In this paper, we study the Pohozaev identity associated with a Heˊ\acute{e}non-Lane-Emden system involving the fractional Laplacian: \begin{equation} \left\{\begin{array}{ll} (-\triangle)^su=|x|^av^p,&x\in\Omega, (-\triangle)^sv=|x|^bu^q,&x\in\Omega, u=v=0,&x\in R^n\backslash\Omega, \end{array} \right. \end{equation} in a star-shaped and bounded domain Ω\Omega for s(0,1)s\in(0,1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases.

Keywords

Cite

@article{arxiv.1604.08258,
  title  = {A Pohozaev Identity for the Fractional H$\acute{e}$non System},
  author = {Pei Ma and Fengquan Li and Yan Li},
  journal= {arXiv preprint arXiv:1604.08258},
  year   = {2017}
}