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Symmetry of Solutions for a Fractional System (1604.01465v2)

Published 6 Apr 2016 in math.AP

Abstract: We consider the following equations: \begin{equation*} \left{\begin{array}{ll} (-\triangle){\alpha/2}u(x)=f(v(x)), \ (-\triangle){\beta/2}v(x)=g(u(x)), &x \in R{n},\ u,v\geq 0, &x \in R{n}, \end{array} \right. \end{equation*} for continuous $f, g$ and $\alpha, \beta \in (0,2)$. Under some natural assumptions on $f$ and $g$, by applying the \emph{method of moving planes} directly to the system, we obtain symmetry on non-negative solutions without any decay assumption on the solutions at infinity.

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