CLASSIFICATION OF POSITIVE SOLUTIONS TO A LANE-EMDEN TYPE INTEGRAL SYSTEM WITH NEGATIVE EXPONENTS

被引：6

作者：

Dou, Jingbo ^{[1
]}

Ren, Fangfang ^{[2
,3
]}

Villavert, John ^{[4
]}

机构：

[1] Xian Univ Finance & Econ, Sch Stat, Xian 710100, Shaanxi, Peoples R China

[2] Cent Univ Finance & Econ, Sch Natl Fiscal Dev, Beijing 100081, Peoples R China

[3] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

[4] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Integral equations; Lane-Emden system; negative exponent; regularity; method of moving spheres; HARDY-LITTLEWOOD-SOBOLEV; LIOUVILLE TYPE; MOVING SPHERES; EQUATIONS; THEOREMS; UNIQUENESS; INEQUALITIES;

D O I：

10.3934/dcds.201694

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we classify the positive solutions to the following Lane-Emden type integral system with negative exponents [GRAPHICS] where n >= 1 is an integer and tau,p,q,r,s > 0. Particularly, using an integral form of the method of moving spheres, we classify the positive solutions to the integral system whenever P vertical bar Q=R vertical bar S=1 vertical bar 2n/tau. We also establish the non-existence of positive solutions under the condition max {p + q,r + s} <= 1 + 2n/tau and p+q+r+s< 2(1 + 2n/tau).

引用

页码：6767 / 6780

页数：14

共 25 条

[1] Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems [J].

Caristi, Gabriella ;

D'Ambrosio, Lorenzo ;

Mitidieri, Enzo .

MILAN JOURNAL OF MATHEMATICS, 2008, 76 (01) :27-67

[2] AN INTEGRAL SYSTEM AND THE LANE-EMDEN CONJECTURE [J].

Chen, Wenxiong ;

Li, Congming .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (04) :1167-1184

[3] Classification of solutions for an integral equation [J].

Chen, WX ;

Li, CM ;

Ou, B .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2006, 59 (03) :330-343

[4] Classification of solutions for a system of integral equations [J].

Chen, WX ;

Li, CM ;

Ou, B .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (1-3) :59-65

[5]

Chen WX, 2005, DISCRETE CONT DYN-A, V12, P347

[6] Reversed Hardy-Littewood-Sobolev Inequality [J].

Dou, Jingbo ;

Zhu, Meijun .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (19) :9696-9726

[7] Sharp Hardy-Littlewood-Sobolev Inequality on the Upper Half Space [J].

Dou, Jingbo ;

Zhu, Meijun .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (03) :651-687

[8] Liouville type theorems for the system of integral equations [J].

Dou, Jingbo .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (06) :2586-2594

[9] Lane-Emden systems with negative exponents [J].

Ghergu, Marius .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (10) :3295-3318

[10] Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications [J].

Han, Yazhou ;

Zhu, Meijun .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (01) :1-25

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