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arXiv · 1704.02190

Symmetry and Nonexistence of Positive Solutions for Fractional Choquard Equations

Pei Ma·Jihui Zhang
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Abstract

This paper is devoted to study the following Choquard equation \begin{eqnarray*}\left\{ \begin{array}{lll} (-\triangle)^{\alpha/2}u=(|x|^{\beta-n}\ast u^p)u^{p-1},~~~&x\in R^n, u\geq0,\,\,&x\in R^n, \end{array} \right. \end{eqnarray*} where $0<\alpha,\beta<2$, $1\leq p<\infty$, and $n\geq2$. Using a direct method of moving planes, we prove the symmetry and nonexistence of positive solutions in the critical and subcritical case respectively.

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Pei Ma, Jihui Zhang. 2017-04-07. Symmetry and Nonexistence of Positive Solutions for Fractional Choquard Equations. https://arxiv.org/abs/1704.02190

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