Some properties of positive solutions for an integral system with the double weighted Riesz potentials

Jiankai Xu; Song Jiang; Huoxiong  Wu

doi:10.3934/cpaa.2016030

Article Contents

2016, Volume 15, Issue 6: 2117-2134. Doi: 10.3934/cpaa.2016030

This issue Previous Article Boundedness and stability of solutions to semi-linear equations and applications to fluid dynamics Next Article Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjoint operators satisfying Gaussian estimates

Some properties of positive solutions for an integral system with the double weighted Riesz potentials

1.
College of Sciences, Hunan Agriculture University, Changsha Hunan 410128
2.
Institute of Applied Physics and Computational Mathematics, P.O.Box 8009-28, Beijing 100088
3.
School of Mathematical Sciences, Xiamen University, Xiamen Fujian 361005

Received: November 30, 2015

Revised: March 31, 2016

Published: October 2016

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Abstract

In this paper, we study some important properties of positive solutions for a nonlinear integral system. With the help of the method of moving planes in an integral form, we show that under certain integrable conditions, all of positive solutions to this system are radially symmetric and decreasing with respect to the origin. Meanwhile, using the regularity lifting lemma, which was recently introduced by Chen and Li in [1], we obtain the optimal integrable intervals and sharp asymptotic behaviors for such positive solutions, which characterize the closeness of system to some extent.

Keywords:

Integral system,
radially symmetry solution,
moving plane method,
regularity lifting lemma,
weighted-Hardy-Littlewood-Sobolev inequality.

Mathematics Subject Classification: 45G15, 45M99, 45G05, 45E10.

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References

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