Symmetry and monotonicity of positive solutions for a class of general pseudo-relativistic systems

Communications on Pure & Applied Analysis Pub Date : 1900-01-01 DOI:10.3934/cpaa.2022045

Xueying Chen, Guanfeng Li, Sijia Bao

引用次数: 1

Abstract

In this paper, we focus on a class of general pseudo-relativistic systems

\begin{document}$ \begin{equation*} \begin{cases} \begin{aligned} &(-\Delta+m^2)^su(x) = f(u(x), v(x)), \\ &(-\Delta+m^2)^tv(x) = g(u(x), v(x)), \end{aligned} \end{cases} \end{equation*} $\end{document}

where \begin{document}$ m \in (0, +\infty) $\end{document} and \begin{document}$ s, t \in (0,1) $\end{document}. Before giving the main results, we first introduce a decay at infinity and a narrow region principle. Then we implement the direct method of moving planes to show the radial symmetry and monotonicity of positive solutions for the above system in both the unit ball and the whole space.

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一类广义伪相对论系统正解的对称性和单调性

In this paper, we focus on a class of general pseudo-relativistic systems \begin{document}$ \begin{equation*} \begin{cases} \begin{aligned} &(-\Delta+m^2)^su(x) = f(u(x), v(x)), \\ &(-\Delta+m^2)^tv(x) = g(u(x), v(x)), \end{aligned} \end{cases} \end{equation*} $\end{document} where \begin{document}$ m \in (0, +\infty) $\end{document} and \begin{document}$ s, t \in (0,1) $\end{document}. Before giving the main results, we first introduce a decay at infinity and a narrow region principle. Then we implement the direct method of moving planes to show the radial symmetry and monotonicity of positive solutions for the above system in both the unit ball and the whole space.

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Communications on Pure & Applied Analysis

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