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

共 50 条

[21] Sign-Changing Solutions of Fractional p-Laplacian Problems
Chang, Xiaojun
Nie, Zhaohu
Wang, Zhi-Qiang
ADVANCED NONLINEAR STUDIES, 2019, 19 (01) : 29 - 53
[22] Optimization problems in rearrangement classes for fractional p-Laplacian equations
Iannizzotto, Antonio
Porru, Giovanni
MATHEMATICS IN ENGINEERING, 2025, 7 (01): : 13 - 34
[23] On a Fractional p-Laplacian Equation with Critical Fractional Sobolev Exponent
Saifia, Ouarda
Velin, Jean
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (04)
[24] On a Fractional p-Laplacian Equation with Critical Fractional Sobolev Exponent
Ouarda Saifia
Jean Vélin
Mediterranean Journal of Mathematics, 2023, 20
[25] Multiplicity results for critical p-Laplacian problems
Barletta, Giuseppina
Candito, Pasquale
Marano, Salvatore A.
Perera, Kanishka
ANNALI DI MATEMATICA PURA ED APPLICATA, 2017, 196 (04) : 1431 - 1440
[26] Fractional p-Laplacian Problem with Critical Stein–Weiss Type Term
Yu Su
The Journal of Geometric Analysis, 2023, 33
[27] A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities
Bhakta, Mousomi
Perera, Kanishka
Firoj, S. K.
ADVANCED NONLINEAR STUDIES, 2023, 23 (01)
[28] Superlinear Kirchhoff-type problems of the fractional p-Laplacian without the (AR) condition
Zuo, Jiabin
An, Tianqing
Li, Mingwei
BOUNDARY VALUE PROBLEMS, 2018,
[29] EXISTENCE OF SOLUTIONS FOR CRITICAL FRACTIONAL p-LAPLACIAN EQUATIONS WITH INDEFINITE WEIGHTS
Cui, Na
Sun, Hong-Rui
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021,
[30] A critical Kirchhoff type problem involving the fractional p-Laplacian in RN
Xiang, Mingqi
Zhang, Binlin
Zhang, Xia
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2018, 63 (05) : 652 - 670

← 1 2 3 4 5 →