EXISTENCE OF POSITIVE SOLUTIONS FOR INTEGRAL SYSTEMS OF THE WEIGHTED HARDY-LITTLEWOOD-SOBOLEV TYPE

被引：5

作者：

Liu, Xiaoqian ^{[1
]}

Lei, Yutian ^{[2
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Inst Math, Nanjing 210023, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Weighted Hardy-Littlewood-Sobolev inequality; integral system; existence of positive solution; Serrin-type condition; SINGULARITY ANALYSIS; ASYMPTOTIC-BEHAVIOR; SHARP CONSTANTS; LIOUVILLE TYPE; SYMMETRY;

D O I：

10.3934/dcds.2020018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the existence/nonexistence of positive solutions of a weighted Hardy-Littlewood-Sobolev type integral system. Such a system is related to the extremal functions of the weighted Hardy-Littlewood-Sobolev inequality. The Serrin-type condition is critical for existence of positive solutions in L-lo(c)infinity (R-n \ {0}). When the Serrin-type condition does not hold, we prove the nonexistence by an iteration process. In addition, we find three pairs of radial solutions when the Serrin-type condition holds. One is singular, and the other two are integrable in R-n and decaying fast and slowly respectively.

引用

页码：467 / 489

页数：23

共 29 条

[21] SOME PROPERTIES OF SOLUTIONS TO THE WEIGHTED HARDY-LITTLEWOOD-SOBOLEV TYPE INTEGRAL SYSTEM [J].

Lu, Yingshu ;

Lu, Zhongxue .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (07) :3791-3810

[22] A Liouville type theorem for an integral system [J].

Ma, Li ;

Chen, Dezhong .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2006, 5 (04) :855-859

[23]

Mitidieri E., 2001, Tr. Mat. Inst. Steklova, V234, P1

[24] On the shape of solutions to an integral system related to the weighted Hardy-Littlewood-Sobolev inequality [J].

Onodera, Michiaki .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (01) :498-510

[25]

Souto MAS., 1995, Differ. Integr. Equ, V8, P1245

[26]

Stein E. M., 1970, PRINCETION MATH SERI, V30

[27]

STEIN EM, 1958, J MATH MECH, V7, P503

[28] Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality [J].

Wu Di ;

Shi ZuoShunHua ;

Yan DunYan .

SCIENCE CHINA-MATHEMATICS, 2014, 57 (05) :963-970

[29] Regularity and symmetry for solutions to a system of weighted integral equations [J].

Zhao, Yonggang .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 391 (01) :209-222

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