EXISTENCE OF WEAK SOLUTIONS FOR NON-LOCAL FRACTIONAL PROBLEMS VIA MORSE THEORY

被引：40

作者：

Ferrara, Massimilianao ^{[1
,2
]}

Bisci, Giovanni Molica ^{[3
]}

Zhang, Binlin ^{[4
]}

机构：

[1] Univ Bocconi Milan, CRIOS, I-89127 Reggio Di Calabria, Italy

[2] Univ Reggio Calabria, I-89127 Reggio Di Calabria, Italy

[3] Univ Mediterranea Reggio Calabria, Dipartimento PAU, I-89127 Reggio Di Calabria, Italy

[4] Heilongjiang Inst Technol, Dept Math, Harbin 150050, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 08期

基金：

黑龙江省自然科学基金;

关键词：

Fractional Laplacian; integro-differential operator; critical groups; Morse theory; NONTRIVIAL SOLUTIONS; LAPLACIAN; EQUATIONS; REGULARITY; BOUNDARY;

D O I：

10.3934/dcdsb.2014.19.2483

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. Non-trivial solutions are obtained by computing the critical groups and Morse theory. Our results extend some classical theorems for semilinear elliptic equations to the non-local fractional setting.

引用

页码：2483 / 2499

页数：17

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