Critical fractional p-Laplacian problems with possibly vanishing potentials

被引：23

作者：

Perera, Kanishka ^{[1
]}

Squassina, Marco ^{[2
]}

Yang, Yang ^{[3
]}

机构：

[1] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

[2] Univ Verona, Dipartimento Informat, I-37134 Verona, Italy

[3] Jiangnan Univ, Sch Sci, Wuxi 214122, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 433卷 / 02期

关键词：

Fractional p-Laplacian; Critical exponent; External potentials; Nontrivial solutions; Generalized linking; Z(2)-cohomological index; NONLINEAR SCHRODINGER-EQUATIONS; EXISTENCE; V(INFINITY)=0; EIGENVALUE;

D O I：

10.1016/j.jmaa.2015.08.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain nontrivial solutions of a critical fractional p-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving critical Sobolev exponents, the problem is further complicated by the absence of a direct sum decomposition suitable for applying classical linking arguments. We overcome this difficulty using a generalized linking construction based on the Z(2)-cohomological index. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：818 / 831

页数：14

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