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 Hnon-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 for . 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}
}