Kirchhoff-Hardy Fractional Problems with Lack of Compactness

被引：80

作者：

Fiscella, Alessio ^{[1
]}

Pucci, Patrizia ^{[2
]}

机构：

[1] Univ Estadual Campinas, IMECC, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil

[2] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy

来源：

ADVANCED NONLINEAR STUDIES | 2017年 / 17卷 / 03期

关键词：

Stationary Kirchhoff-Dirichlet Problems; Nonlocal p-Laplacian Operators; Hardy Coefficients; Critical Nonlinearities; Variational Methods; EXISTENCE; EQUATIONS; BREZIS;

D O I：

10.1515/ans-2017-6021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator and involving a Hardy potential and different critical nonlinearities. In particular, we cover the delicate degenerate case, that is, when the Kirchhoff function M is zero at zero. To overcome the difficulties due to the lack of compactness as well as the degeneracy of the models, we have to make use of different approaches.

引用

页码：429 / 456

页数：28

共 33 条

[1] [Anonymous], 1985, MONOGR STUD MATH
[2] Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
Autuori, Giuseppina
Fiscella, Alessio
Pucci, Patrizia
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 125 : 699 - 714
[3] Existence of entire solutions for a class of quasilinear elliptic equations
Autuori, Giuseppina
Pucci, Patrizia
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03): : 977 - 1009
[4] Bisci GM, 2016, ENCYCLOP MATH APPL, V162
[5] Bisci GM, 2015, ADV DIFFERENTIAL EQU, V20, P635
[6] Bogachev V. I., 2007, MEASURE THEORY, V2, DOI DOI 10.1007/978-3-540-34514-5
[7] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS
BREZIS, H
LIEB, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) : 486 - 490
[8] Caffarelli LA, 2009, ICIAM 07: 6TH INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS, P43
[9] Existence theorems for entire solutions of stationary Kirchhoff fractional p-Laplacian equations
Caponi, Maicol
Pucci, Patrizia
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2016, 195 (06) : 2099 - 2129
[10] Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations
Colasuonno, Francesca
Pucci, Patrizia
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) : 5962 - 5974

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