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

[1] Positive solutions for a quasilinear elliptic equation of Kirchhoff type [J].

Alves, CO ;

Corrêa, FJSA ;

Ma, TF .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (01) :85-93

[2]

Bisci GM, 2016, ENCYCLOP MATH APPL, V162

[3] Applications of local linking to nonlocal Neumann problems [J].

Bisci, Giovanni Molica ;

Radulescu, Vicentiu D. .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2015, 17 (01)

[4] MOUNTAIN PASS SOLUTIONS FOR NONLOCAL EQUATIONS [J].

Bisci, Giovanni Molica ;

Radulescu, Vicentiu D. .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2014, 39 (02) :579-592

[5] REMARKS ON SUBLINEAR ELLIPTIC-EQUATIONS [J].

BREZIS, H ;

OSWALD, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1986, 10 (01) :55-64

[6]

CAFFARELLI L, 1984, COMPOS MATH, V53, P259

[7]

Catrina F, 2001, COMMUN PUR APPL MATH, V54, P229, DOI 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO

[8]

2-I

[9] Weak Solutions and Energy Estimates for Singular p-Laplacian-Type Equations [J].

Chu, Jifeng ;

Heidarkhani, Shapour ;

Salari, Amjad ;

Caristi, Giuseppe .

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2018, 24 (01) :51-63

[10] WEAK SOLUTIONS AND ENERGY ESTIMATES FOR A DEGENERATE NONLOCAL PROBLEM INVOLVING SUB-LINEAR NONLINEARITIES [J].

Chu, Jifeng ;

Heidarkhani, Shapour ;

Kou, Kit Ian ;

Salari, Amjad .

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (05) :1573-1594

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