Narrow region principle and Liouville type results for fractional Lane-Emden system

被引：3

作者：

Cai, Miaomiao ^{[1
]}

Mei, Linfeng ^{[1
]}

机构：

[1] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang, Peoples R China

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2017年 / 62卷 / 07期

基金：

美国国家科学基金会;

关键词：

Fractional Lane-Emden system; narrow region principle; moving planes; radial symmetry; non-existence; NONLINEAR ELLIPTIC-EQUATIONS; RADIAL SYMMETRY; POSITIVE SOLUTIONS; CLASSIFICATION; MONOTONICITY;

D O I：

10.1080/17476933.2016.1258066

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, narrow region principle for cooperative systems involving fractional Laplacian is developed. As an application, some Liouville type results of the fractional Lane- Emden system ( - ) a/ 2u( x) = vp( x), ( - ) a/ 2v( x) = uq( x) ( 1) are obtained via the method of moving planes. Different to the conventional method by studying the equivalent integral system, we work directly on the differential system. Our method can also be employed to obtain Liouville type results for general cooperative systems involving fractional Laplacian.

引用

页码：1002 / 1014

页数：13

共 32 条

[1]

[Anonymous], 1996, DIFFER INTEGRAL EQU

[2]

[Anonymous], 1996, Differ. Integral Equ.

[3] A concave-convex elliptic problem involving the fractional Laplacian [J].

Braendle, C. ;

Colorado, E. ;

de Pablo, A. ;

Sanchez, U. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (01) :39-71

[4] Symmetry results for semilinear elliptic systems in the whole space [J].

Busca, J ;

Sirakov, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 163 (01) :41-56

[5] ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH [J].

CAFFARELLI, LA ;

GIDAS, B ;

SPRUCK, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (03) :271-297

[6] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[7]

Chen W, 2014, ARXIV14111697V1MATHA

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

Chen, Wenxiong ;

Li, Congming .

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

[9] CLASSIFICATION OF SOLUTIONS OF SOME NONLINEAR ELLIPTIC-EQUATIONS [J].

CHEN, WX ;

LI, CM .

DUKE MATHEMATICAL JOURNAL, 1991, 63 (03) :615-622

[10] 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

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