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

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