Jian Wang, Xin Wei, Symmetric property of positive solutions to systems involving non-local operators, 2016 (2016), Article ID 18 (10 April 2016)

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Abstract

In this paper, we study symmetry results of positive solutions for the following system involving nonlocal operators $(-\Delta+id)^{\alpha_1} u$ $=f_1(v)$ in $\mathbb{R}^N,$ $(-\Delta+id)^{\alpha_2} u$ $=f_2(v)$ in $\mathbb{R}^N,$ $\lim_{|x|\to+\infty}u(x)$ $=\lim_{|x|\to+\infty}v(x)=0,$ where $N\geq2$ and $0<\alpha_1,$ $\alpha_2<1$. We use the method of moving planes to obtain the radial symmetry of positive solutions to the above system.