Liouville-type theorem for higher-order Hardy-Hénon system

Kui Li; Zhitao Zhang

doi:10.3934/cpaa.2021134

Article Contents

2021, Volume 20, Issue 11: 3851-3869. Doi: 10.3934/cpaa.2021134 open access

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Liouville-type theorem for higher-order Hardy-Hénon system

Kui Li^1, and
Zhitao Zhang^2,3,4, ,

1.
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China
2.
School of Mathematical Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
3.
HLM, Academy of Mathematics and Systems Science of Sciences, Chinese Academy of Sciences, Beijing 100190, China
4.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^* Corresponding author
^* Corresponding author

Received: December 31, 2020

Revised: April 30, 2021

Early access: August 2021

Published: November 2021

Supported by NSF of China (No. 11771428, 11901535, 12031015, 12026217)

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Abstract

In this paper, we study higher-order Hardy-Hénon elliptic systems with weights. We first prove a new theorem on regularities of the positive solutions at the origin, then study equivalence between the higher-order Hardy-Hénon elliptic system and a proper integral system, and we obtain a new and interesting Liouville-type theorem by methods of moving planes and moving spheres for integral system. We also use this Liouville-type theorem to prove the Hénon-Lane-Emden conjecture for polyharmonic system under some conditions.

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Mathematics Subject Classification: Primary: 35J30, 35J75, 35B53.

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