Existence and Nonexistence of Solutions for Fourth-Order Nonlinear Difference Boundary Value Problems via Variational Methods

被引：0

作者：

Liu, Xia ^{[1
,2
,3
]}

Zhou, Tao ^{[4
]}

Shi, Haiping ^{[5
,6
]}

机构：

[1] Guangdong Univ Foreign Studies, Coll Continuing Educ, Guangzhou 510420, Guangdong, Peoples R China

[2] Guangdong Univ Foreign Studies, Open Coll, Guangzhou 510420, Guangdong, Peoples R China

[3] Hunan Agr Univ, Sci Coll, Changsha 410128, Hunan, Peoples R China

[4] South China Normal Univ, Sch Econ & Management, Guangzhou 510006, Guangdong, Peoples R China

[5] Guangdong Construct Polytech, Modern Business & Management Dept, Guangzhou 510440, Guangdong, Peoples R China

[6] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2018年 / 2018卷

基金：

中国国家自然科学基金;

关键词：

HOMOCLINIC ORBITS; SUBHARMONIC SOLUTIONS; EQUATIONS;

D O I：

10.1155/2018/6703503

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with boundary value problems for a fourth-order nonlinear difference equation. Via variational methods and critical point theory, sufficient conditions are obtained for the existence of at least two nontrivial solutions, the existence of n distinct pairs of nontrivial solutions, and nonexistence of solutions. Some examples are provided to show the effectiveness of the main results.

引用

下载

页数：9

共 50 条

[21] EXISTENCE AND LOCALIZATION OF SOLUTIONS FOR FOURTH-ORDER BOUNDARY-VALUE PROBLEMS
Enguica, Ricardo
Sanchez, Luis
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[22] Existence of solutions for some fourth-order boundary value problems with parameters
Yang, Yang
Zhang, Jihui
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (04) : 1364 - 1375
[23] Fourth-order compact finite difference method for fourth-order nonlinear elliptic boundary value problems
Wang, Yuan-Ming
Guo, Ben-Yu
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 221 (01) : 76 - 97
[24] Existence of multiple solutions of fourth-order difference equation boundary value problem
Cai, Xiaochun
[J]. INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2009, 2 (3-4) : 273 - 279
[25] Existence of nontrivial solutions for a nonlinear fourth-order boundary value problem via iterative method
Zhai, Chengbo
Jiang, Chunrong
[J]. JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (06): : 4295 - 4304
[26] POSITIVE SOLUTIONS OF NONLINEAR FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS
LüHaiyan (Dept.of Math.
[J]. Annals of Applied Mathematics, 2007, (03) : 288 - 296
[27] Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems
Lin, Longfei
Liu, Yansheng
Zhao, Daliang
[J]. SYMMETRY-BASEL, 2020, 12 (12): : 1 - 13
[28] Positive solutions of fourth-order nonlinear singular boundary value problems
Xu, Fuyi
Su, Hua
Zhang, Xiaoyan
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (05) : 1284 - 1297
[29] Nonzero Solutions for Nonlinear Systems of Fourth-Order Boundary Value Problems
Agarwal, Ravi P.
Jleli, Mohamed
Samet, Bessem
[J]. JOURNAL OF MATHEMATICS, 2021, 2021
[30] NODAL SOLUTIONS OF SOME NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
Aliyeva, Yagut N.
[J]. PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2024, 50 (01): : 104 - 114

← 1 2 3 4 5 →