Liouville theorems for fractional  Hénon equation and system on $\mathbb{R}^n$

Jingbo Dou; Huaiyu  Zhou

doi:10.3934/cpaa.2015.14.1915

Article Contents

2015, Volume 14, Issue 5: 1915-1927. Doi: 10.3934/cpaa.2015.14.1915

This issue Previous Article Low regularity well-posedness for Gross-Neveu equations Next Article Homoclinic orbits for discrete Hamiltonian systems with indefinite linear part

Liouville theorems for fractional Hénon equation and system on $\mathbb{R}^n$

Jingbo Dou^1, and
Huaiyu Zhou^1,

1.
School of Statistics, Xi'an University of Finance and Economics, Xi'an, Shaanxi, 710100

Received: October 2014

Revised: April 2015

Published: September 2015

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Abstract

In this paper, we establish some Liouville type theorems for positive solutions of fractional Hénon equation and system in $\mathbb{R}^n$. First, under some regularity conditions, we show that the above equation and system are equivalent to the some integral equation and system, respectively. Then, we prove Liouville type theorems via the method of moving planes in integral forms.

Keywords:

Weighted Hardy-Littlewood-Sobolev inequality,
Hénon equation,
Liouville type theorem,
method of moving planes.

Mathematics Subject Classification: Primary: 35B53; Secondary: 35B06.

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