Higher nonlocal problems with bounded potential

被引：64

作者：

Bisci, Giovanni Molica ^{[1
]}

Repovs, Dusan ^{[2
,3
]}

机构：

[1] Univ Mediterranea Reggio Calabria, Dipartimento PAU, I-89124 Reggio Di Calabria, Italy

[2] Univ Ljubljana, Fac Educ, Ljubljana, Slovenia

[3] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 420卷 / 01期

关键词：

Fractional equations; Multiple solutions; Critical points results; KIRCHHOFF SYSTEMS; OPERATORS; EQUATIONS;

D O I：

10.1016/j.jmaa.2014.05.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to study a class of nonlocal fractional Laplacian equations depending on two real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci, we establish the existence of three weak solutions for nonlocal fractional problems exploiting an abstract critical point result for smooth functionals. We emphasize that the dependence of the underlying equation from one of the real parameters is not necessarily of affine type. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：167 / 176

页数：10

共 18 条

[1]

[Anonymous], 2010, ENCY MATH APPL

[2] Local asymptotic stability for polyharmonic Kirchhoff systems [J].

Autuori, G. ;

Pucci, P. .

APPLICABLE ANALYSIS, 2011, 90 (3-4) :493-514

[3] Elliptic problems involving the fractional Laplacian in RN [J].

Autuori, Giuseppina ;

Pucci, Patrizia .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (08) :2340-2362

[4] Existence of entire solutions for a class of quasilinear elliptic equations [J].

Autuori, Giuseppina ;

Pucci, Patrizia .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03) :977-1009

[5] Kirchhoff systems with dynamic boundary conditions [J].

Autuori, Giuseppina ;

Pucci, Patrizia .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (07) :1952-1965

[6] KIRCHHOFF SYSTEMS WITH NONLINEAR SOURCE AND BOUNDARY DAMPING TERMS [J].

Autuori, Giuseppina ;

Pucci, Patrizia .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2010, 9 (05) :1161-1188

[7] Fractional equations with bounded primitive [J].

Bisci, Giovanni Molica .

APPLIED MATHEMATICS LETTERS, 2014, 27 :53-58

[8]

Cabre X., 2014, T AM MATH S IN PRESS

[9] Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates [J].

Cabre, Xavier ;

Sire, Yannick .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01) :23-53

[10] Positive solutions of nonlinear problems involving the square root of the Laplacian [J].

Cabre, Xavier ;

Tan, Jinggang .

ADVANCES IN MATHEMATICS, 2010, 224 (05) :2052-2093

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