Homoclinic solutions for nonlinear general fourth-order differential equations

被引：3

作者：

Carrasco, Hugo ^{[1
]}

Minhos, Feliz ^{[1
,2
]}

机构：

[1] Univ Evora, Dept Matemat, Escola Ciencias & Tecnol, Evora, Portugal

[2] Univ Evora, CIMA, Inst Invest Formacao Avancada, P-7000671 Evora, Portugal

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 16期

关键词：

higher-order problems in the real line; fixed point theory; Green's functions; homoclinic solutions; beams on nonuniform elastic foundations; SWIFT-HOHENBERG;

D O I：

10.1002/mma.4426

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work provides sufficient conditions for the existence of homoclinic solutions of fourth-order nonlinear ordinary differential equations. Using Green's functions, we formulate a new modified integral equation that is equivalent to the original nonlinear equation. In an adequate function space, the corresponding nonlinear integral operator is compact, and it is proved an existence result by Schauder's fixed point theorem. Copyright (c) 2017 John Wiley & Sons, Ltd.

引用

页码：5768 / 5776

页数：9

共 50 条

[1] Multiplicity of Homoclinic Solutions for a Class of Nonperiodic Fourth-Order Differential Equations with General Perturbation
Yang, Liu
[J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
[2] Homoclinic solutions for a class of fourth-order difference equations
Shi, Haiping
Liu, Xia
Zhang, Yuanbiao
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (10) : 2617 - 2625
[3] Ground State Homoclinic Solutions for a Class of Superquadratic Fourth-Order Differential Equations
Mohsen Timoumi
[J]. Differential Equations and Dynamical Systems, 2024, 32 : 401 - 420
[4] Ground State Homoclinic Solutions for a Class of Superquadratic Fourth-Order Differential Equations
Timoumi, Mohsen
[J]. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2024, 32 (02) : 401 - 420
[5] INFINITELY MANY HOMOCLINIC SOLUTIONS FOR A CLASS OF SUPERQUADRATIC FOURTH-ORDER DIFFERENTIAL EQUATIONS
Timoumi, Mohsen
[J]. JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2018, 2018
[6] INFINITELY MANY HOMOCLINIC SOLUTIONS FOR DIFFERENT CLASSES OF FOURTH-ORDER DIFFERENTIAL EQUATIONS
Timoumi, Mohsen
[J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 37 (01): : 137 - 161
[7] Periodic solutions of some fourth-order nonlinear differential equations
Fan, Qiyi
Wang, Wentao
Zhou, Jinglei
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (02) : 121 - 126
[8] Nonlinear fourth-order differential equations with solutions in the form of transcendents
N. A. Kudryashov
[J]. Theoretical and Mathematical Physics, 2000, 122 : 58 - 71
[9] Nonlinear fourth-order differential equations with solutions in the form of transcendents
Kudryashov, NA
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2000, 122 (01) : 58 - 71
[10] Periodic solutions for a class of fourth-order nonlinear differential equations
Zhao, Changhong
Chen, Wei
Zhou, Jinglei
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1221 - 1226

← 1 2 3 4 5 →