The Liouville type theorem and local regularity results for nonlineardifferential and integral systems

Zhenjie Li; Ze Cheng; Dongsheng Li

doi:10.3934/cpaa.2015.14.565

Article Contents

2015, Volume 14, Issue 2: 565-576. Doi: 10.3934/cpaa.2015.14.565

This issue Previous Article Singularity formation for relativistic Euler and Euler-Poisson equations with repulsive force Next Article On the growth of the energy of entire solutions to the vector Allen-Cahn equation

The Liouville type theorem and local regularity results for nonlinear differential and integral systems

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049
2.
Department of Applied Mathematics, University of Colorado at Boulder, Colorado

Received: April 2014

Revised: November 2014

Published: March 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we establish a Liouville type theorem for positive solutions of a class of system of integral equations. Firstly, we show the local regularity lifting result with the help of the Hardy-Littlewood-Sobolev inequality. Then by the method of moving planes in integral forms, we obtain a Liouville type theorem for this system.

Keywords:

Louville type theorem,
integral systems,
method of moving planes of integral form,
weighted Hardy-Littlewood-Sobolev inequality.

Mathematics Subject Classification: Primary: 35A05, 35J45, 35J60; Secondary: 45G15.

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