Positive solutions of integral systems involving Bessel potentials

Yutian Lei

doi:10.3934/cpaa.2013.12.2721

Article Contents

2013, Volume 12, Issue 6: 2721-2737. Doi: 10.3934/cpaa.2013.12.2721

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Positive solutions of integral systems involving Bessel potentials

Yutian Lei^1,

1.
School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210097

Received: September 30, 2012

Revised: November 30, 2012

Published: October 2013

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Abstract

This paper is concerned with integral systems involving the Bessel potentials. Such integral systems are helpful to understand the corresponding PDE systems, such as some static Shrödinger systems with the critical and the supercritical exponents. We use the lifting lemma on regularity to obtain an integrability interval of solutions. Since the Bessel kernel does not have singularity at infinity, we extend the integrability interval to the whole $[1,\infty]$. Next, we use the method of moving planes to prove the radial symmetry for the positive solution of the system. Based on these results, by an iteration we obtain the estimate of the exponential decay of those solutions near infinity. Finally, we discuss the uniqueness of the positive solution of PDE system under some assumption.

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Mathematics Subject Classification: Primary: 45E10, 45G05.

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