Multiple solutions for degenerate nonlocal problems

被引：14

作者：

Caristi, Giuseppe ^{[1
]}

Heidarkhani, Shapour ^{[2
]}

Salari, Amjad ^{[3
]}

Tersian, Stepan A. ^{[4
]}

机构：

[1] Univ Messina, Dept Econ, Via Verdi 75, Messina, Italy

[2] Razi Univ, Fac Sci, Dept Math, Kermanshah 67149, Iran

[3] Islamic Azad Univ, Kermanshah Branch, Young Researchers & Elite Club, Kermanshah, Iran

[4] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev Str 8, BU-1113 Sofia, Bulgaria

来源：

APPLIED MATHEMATICS LETTERS | 2018年 / 84卷

关键词：

p-Laplacian operator; Nonlocal problem; Singularity; Multiple solutions; Critical point theory; KIRCHHOFF-TYPE PROBLEMS; POSITIVE SOLUTIONS; WEAK SOLUTIONS; INEQUALITIES;

D O I：

10.1016/j.aml.2018.04.007

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 solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at the origin or perturbation property. We obtain some new criteria for existence of two and infinitely many solutions of the problem using critical point theory. Some recent results are extended and improved. Some examples are presented to demonstrate the application of our main results. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：26 / 33

页数：8

共 28 条

[11] A Variational Approach to a Kirchhoff-type Problem Involving Two Parameters [J].

Graef, John R. ;

Heidarkhani, Shapour ;

Kong, Lingju .

RESULTS IN MATHEMATICS, 2013, 63 (3-4) :877-889

[12] Infinitely many positive solutions for Kirchhoff-type problems [J].

He, Xiaoming ;

Zou, Wenming .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (03) :1407-1414

[13] Infinitely many solutions for systems of n two-point Kirchhoff-type boundary value problems [J].

Heidarkhani, Shapour .

ANNALES POLONICI MATHEMATICI, 2013, 107 (02) :133-152

[14]

Kirchhoff G., 1883, VORLESUNGEN MATH PHY

[15] Sign-changing and multiple solutions of Kirchhoff type problems without the PS condition [J].

Mao, Anmin ;

Zhang, Zhitao .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (03) :1275-1287

[16]

Mawhin J., 1989, Applied Mathematical Sciences

[17]

MOLICABISCI G, 2015, TOPOL METHOD NONL AN, V45, P493

[18]

Motreanu D., 2003, NONCONVEX OPTIMIZATI

[19] MULTIPLE SOLUTIONS FOR A CLASS OF DEGENERATE NONLOCAL PROBLEMS INVOLVING SUBLINEAR NONLINEARITIES [J].

Nguyen Thanh Chung ;

Hoang Quoc Toan .

MATEMATICHE, 2014, 69 (02) :171-182

[20] Nontrivial solutions of Kirchhoff-type problems via the Yang index [J].

Perera, K ;

Zhang, ZT .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 221 (01) :246-255

← 1 2 3 →