Liouville type theorem to an integral system in the half-space

Weiwei Zhao; Jinge Yang; Sining Zheng

doi:10.3934/cpaa.2014.13.511

Article Contents

2014, Volume 13, Issue 2: 511-525. Doi: 10.3934/cpaa.2014.13.511

This issue Previous Article Schrödinger-like operators and the eikonal equation Next Article Well-posedness for the supercritical gKdV equation

Liouville type theorem to an integral system in the half-space

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024
2.
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024

Received: July 2012

Revised: June 2013

Published: March 2014

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Abstract

In this paper, by using the moving plane method in integral forms, we establish a Liouville type theorem for a coupled integral system with Navier boundary values in the half-space. Furthermore, we prove that the Liouville type theorem is valid for the related differential system as well under an additional assumption by showing the equivalence between the involved differential and integral systems.

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Mathematics Subject Classification: Primary: 35B53; 35J40; Secondary: 35J60.

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