Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-30
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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 Zhuo and Li, 2011.
American Psychological Association (APA)
Cao, Linfen& Dai, Zhaohui. 2014. Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1033854
Modern Language Association (MLA)
Cao, Linfen& Dai, Zhaohui. Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space. Abstract and Applied Analysis No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-1033854
American Medical Association (AMA)
Cao, Linfen& Dai, Zhaohui. Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1033854
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033854