scholarly journals A Liouville-type theorem for an integral system on a half-space R + n

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Linfen Cao ◽  
Zhaohui Dai
Keyword(s):  
Half Space ◽  
Type Theorem ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Integral System

A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhao Liu ◽  
Wei Dai
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dirichlet Boundary ◽  
Type Theorem ◽  
Dirichlet Boundary Conditions ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harmonic System

AbstractIn this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝwherewhereis the Green’s function in ℝ

Liouville type theorem for higher order Hénon equations on a half space

2019 ◽  
Vol 183 ◽  
pp. 284-302 ◽  
Author(s):  
Wei Dai ◽  
Guolin Qin ◽  
Yang Zhang
Keyword(s):  
Half Space ◽  
Type Theorem ◽  
Higher Order ◽  
Liouville Type ◽  
Liouville Type Theorem

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kui Li ◽  
Zhitao Zhang
Keyword(s):  
Elliptic System ◽  
Type Theorem ◽  
Elliptic Systems ◽  
Higher Order ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Integral System ◽  
Moving Planes ◽  
Polyharmonic System ◽  
Moving Spheres

<p style='text-indent:20px;'>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.</p>

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