Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space

Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space

We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and subcritical cases under some integrability cond...

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Main Authors: Linfen Cao, Zhaohui Dai
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/593210
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spelling doaj-a30d47de61db4fc9b562a163d47a4d4d2020-11-24T22:38:45ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/593210593210Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half SpaceLinfen Cao0Zhaohui Dai1College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaDepartment of Computer Science, Henan Normal University, Xinxiang, Henan 453007, ChinaWe consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and subcritical cases under some integrability conditions. Ruling out these nonexistence results, we also discuss the positive solutions of the integral system in critical case. By the method of moving planes, we show that a pair of positive solutions to such system is rotationally symmetric about xn-axis, which is much more general than the main result of Zhuo and Li, 2011.http://dx.doi.org/10.1155/2014/593210
collection DOAJ
language English
format Article
sources DOAJ
author Linfen Cao
Zhaohui Dai
spellingShingle Linfen Cao
Zhaohui Dai
Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
Abstract and Applied Analysis
author_facet Linfen Cao
Zhaohui Dai
author_sort Linfen Cao
title Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
title_short Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
title_full Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
title_fullStr Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
title_full_unstemmed Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
title_sort symmetry and nonexistence of positive solutions for weighted hls system of integral equations on a half space
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and subcritical cases under some integrability conditions. Ruling out these nonexistence results, we also discuss the positive solutions of the integral system in critical case. By the method of moving planes, we show that a pair of positive solutions to such system is rotationally symmetric about xn-axis, which is much more general than the main result of Zhuo and Li, 2011.
url http://dx.doi.org/10.1155/2014/593210
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AT zhaohuidai symmetryandnonexistenceofpositivesolutionsforweightedhlssystemofintegralequationsonahalfspace
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