Symmetry results for systems involving fractional Laplacian

Xiongjun Zheng () and Jian Wang ()
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Xiongjun Zheng: Jiangxi Normal University
Jian Wang: Jiangxi Normal University

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 1, 39-52

Abstract: Abstract In this paper we investigate symmetry results for positive solutions of systems involving the fractional Laplacian (1) $\left\{ \begin{gathered} ( - \Delta )^{\alpha _1 } u_1 (x) = f_1 (u_2 (x)),x \in \mathbb{R}^\mathbb{N} , \hfill \\ ( - \Delta )^{\alpha _2 } u_2 (x) = f_2 (u_1 (x)),x \in \mathbb{R}^\mathbb{N} , \hfill \\ \lim _{|x| \to \infty } u_1 (x) = \lim _{|x| \to \infty } u_2 (x) = 0 \hfill \\ \end{gathered} \right. $ where N ≥ 2 and α 1, α 2 ∈ (0, 1). We prove symmetry properties by the method of moving planes.

Keywords: Fractional Laplacian; moving planes; system; radial symmetry (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0050-2

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