Liouville type theorems for fractional and higher-order fractional systems

Daomin Cao; Guolin Qin

doi:10.3934/dcds.2020361

Article Contents

2021, Volume 41, Issue 5: 2269-2283. Doi: 10.3934/dcds.2020361

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Liouville type theorems for fractional and higher-order fractional systems

Daomin Cao^1,2, and
Guolin Qin^3,4,

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510405, China
2.
Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China
3.
Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100190, China
4.
University of Chinese Academy of sciences, Beijing 100049, China

Received: April 30, 2020

Revised: July 31, 2020

Early access: October 2020

Published: May 2021

D. Cao was supported by NNSF of China (No.11831009) and Chinese Academy of Sciences (No.QYZDJ-SSW-SYS021)

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Abstract

In this paper, we first establish decay estimates for the fractional and higher-order fractional Hénon-Lane-Emden systems by using a nonlocal average and integral estimates, which deduce a result of non-existence. Next, we apply the method of scaling spheres introduced in [16] to derive a Liouville type theorem. We also construct an interesting example on super $ \frac{\alpha}{2} $-harmonic functions (Proposition 1.2).

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Mathematics Subject Classification: Primary: 35J61; Secondary: 35B53, 35C15.

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