Symmetry and nonexistence of positive solutions for weighted HLS system of integral equations on a half space
type: Item
instance of: scholarly article
title: Symmetry and nonexistence of positive solutions for weighted HLS system of integral equations on a half space
zbMATH Open document ID: 1474.45039
DOI: 10.1155/2014/593210
author: Linfen Cao
author: Zhaohui Dai
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 \(x_n\)-axis, which is much more general than the main result of \textit{R. Zhuo} and \textit{D. Li} [J. Math. Anal. Appl. 381, No. 1, 392--401 (2011; Zbl 1220.45005)].
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45M20
zbMATH DE Number: 7022673
Wikidata QID: Q59039727
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/593210
OpenAlex ID: W1992157048
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description: scientific article; zbMATH DE number 7022673