A LIOUVILLE THEOREM FOR INDEFINITE FRACTIONAL DIFFUSION EQUATIONS AND ITS APPLICATION TO EXISTENCE OF SOLUTIONS

被引：4

作者：

Barrios, Begona ^{[1
]}

Del Pezzo, Leandro ^{[2
]}

Garcia-Melian, Jorge ^{[1
,3
]}

Quaas, Alexander ^{[4
]}

机构：

[1] Univ La Laguna, Dept Anal Matemat, C Astrofis Francisco Sanchez S-N, San Cristobal la Laguna 38200, Spain

[2] Univ Torcuato Tella, CONICET, Dept Matemat & Estadist, Ave Figueroa Alcorta 7350,C1428BCW, Ca De Buenos Aires, Argentina

[3] Univ La Laguna, Inst Univ Estudios Avanzados IUdEA Fis Atom Mol &, C Astrofis Francisco Sanchez S-N, San Cristobal la Laguna 38200, Spain

[4] Univ Tecn Federico Santa Maria, Dept Matemat, Casilla 5-110,Avda Espana, Valparaiso 1680, Chile

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 11期

关键词：

Liouville theorem; fractional Laplacian; positive solution; a priori bounds; SEMILINEAR ELLIPTIC-EQUATIONS; MOVING PLANES; R-N; REGULARITY; NONLINEARITIES; CLASSIFICATION; LAPLACIAN; SIGN;

D O I：

10.3934/dcds.2017248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we obtain a Liouville theorem for positive, bounded solutions of the equation (Delta)(s) u = h (x (N)) f (u) in R-N where (-Delta)(s) stands for the fractional Laplacian with s is an element of (0; 1), and the functions h and f are nondecreasing. The main feature is that the function h changes sign in R, therefore the problem is sometimes termed as indefinite. As an application we obtain a priori bounds for positive solutions of some boundary value problems, which give existence of such solutions by means of bifurcation methods.

引用

页码：5731 / 5746

页数：16

共 50 条

[41] Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions
An, Jiaxing
Dou, Jingbo
Hu, Yunyun
BULLETIN OF MATHEMATICAL SCIENCES, 2024,
[42] EXISTENCE AND REGULARITY OF SOLUTIONS TO 1-D FRACTIONAL ORDER DIFFUSION EQUATIONS
Jia, Lueling
Chen, Huanzhen
Ervin, Vincent J.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2019,
[43] Liouville-type Theorem for Fractional Kirchhoff Equations with Weights
Anh Tuan Duong
Duc Hiep Pham
Bulletin of the Iranian Mathematical Society, 2021, 47 : 1585 - 1597
[44] Liouville-type Theorem for Fractional Kirchhoff Equations with Weights
Duong, Anh Tuan
Pham, Duc Hiep
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2021, 47 (05) : 1585 - 1597
[45] A Liouville theorem and radial symmetry for dual fractional parabolic equations
Guo, Yahong
Ma, Lingwei
Zhang, Zhenqiu
ANALYSIS AND APPLICATIONS, 2024, 22 (04) : 791 - 814
[46] Liouville theorem of the regional fractional Lane-Emden equations
Wang, Ying
Sun, Yanqing
Chen, Hongxing
Hajaiej, Hichem
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024,
[47] Liouville property and existence of entire solutions of Hessian equations
Wang, Cong
Bao, Jiguang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 223
[48] Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices
Zhao, Caidi
Jiang, Huite
Caraballo, Tomás
Applied Mathematics and Computation, 2021, 404
[49] Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices
Zhao, Caidi
Jiang, Huite
Caraballo, Tomas
APPLIED MATHEMATICS AND COMPUTATION, 2021, 404
[50] EXISTENCE OF GLOBAL SOLUTIONS AND BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF FRACTIONAL DIFFUSION EQUATIONS
Ahmad, Bashir
Alsaedi, Ahmed
Berbiche, Mohamed
Kirane, Mokhtar
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2020,

← 1 2 3 4 5 →