PROPERTIES OF POSITIVE SOLUTIONS FOR THE FRACTIONAL LAPLACIAN SYSTEMS WITH POSITIVE-NEGATIVE MIXED POWERS

被引：0

作者：

Lu, Zhongxue ^{[1
]}

Niu, Mengjia ^{[1
]}

Shen, Yuanyuan ^{[1
]}

Yuan, Anjie ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 61卷 / 03期

关键词：

The fractional Laplacian; positive-negative mixed powers; method of moving planes; radial symmetry; monotonicity; MOVING PLANES; MAXIMUM-PRINCIPLES; RADIAL SYMMETRY; P-LAPLACIAN; NONEXISTENCE; MONOTONICITY;

D O I：

10.4134/JKMS.j230232

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive -negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive -negative mixed powers in the whole space. We also give two special cases.

引用

页码：445 / 459

页数：15

共 38 条

[1]

Applebaum D., 2004, Notices Amer Math Soc, V51, P1336

[2] Semilinear problems for the fractional laplacian with a singular nonlinearity [J].

Barrios, Begona ;

De Bonis, Ida ;

Medina, Maria ;

Peral, Ireneo .

OPEN MATHEMATICS, 2015, 13 :390-407

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

Caffarelli, Luis ;

Silvestre, Luis .

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

[5] MOVING PLANES FOR NONLINEAR FRACTIONAL LAPLACIAN EQUATION WITH NEGATIVE POWERS [J].

Cai, Miaomiao ;

Ma, Li .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (09) :4603-4615

[6] RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO A CLASS OF FRACTIONAL LAPLACIAN WITH A SINGULAR NONLINEARITY [J].

Cao, Linfen ;

Wang, Xiaoshan .

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2021, 58 (06) :1449-1460

[7]

Chen W., 2019, The Fractional Laplacian, P350, DOI DOI 10.1142/10550

[8] Maximum principles for the fractional p-Laplacian and symmetry of solutions [J].

Chen, Wenxiong ;

Li, Congming .

ADVANCES IN MATHEMATICS, 2018, 335 :735-758

[9] A direct method of moving spheres on fractional order equations [J].

Chen, Wenxiong ;

Li, Yan ;

Zhang, Ruobing .

JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (10) :4131-4157

[10] A direct method of moving planes for the fractional Laplacian [J].

Chen, Wenxiong ;

Li, Congming ;

Li, Yan .

ADVANCES IN MATHEMATICS, 2017, 308 :404-437

← 1 2 3 4 →