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 19 条

[1]

Adams G, 1986, J ENG MECH, V113, P542

[2]

Amick CJ, 1992, European J Appl Math, V3, P97, DOI DOI 10.1017/S0956792500000735

[3]

[Anonymous], 1973, Integral Equations and Stability of Feedback Systems

[4]

[Anonymous], 1986, FIXED POINT THEOREMS

[5]

Blackmore A, 1996, T ASME, V63, P234

[6] Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity [J].

Bonheure, D .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2004, 21 (03) :319-340

[7] NATURE OF SPATIAL CHAOS [J].

COULLET, P ;

ELPHICK, C ;

REPAUX, D .

PHYSICAL REVIEW LETTERS, 1987, 58 (05) :431-434

[8] STRUCTURAL LOCALIZATION PHENOMENA AND THE DYNAMICAL PHASE-SPACE ANALOGY [J].

HUNT, GW ;

BOLT, HM ;

THOMPSON, JMT .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1989, 425 (1869) :245-267

[9] A new semi-analytical approach to large deflections of Bernoulli-Euler-v. Karman beams on a linear elastic foundation: Nonlinear analysis of infinite beams [J].

Jang, T. S. .

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2013, 66 :22-32

[10] SWIFT-HOHENBERG EQUATION FOR LASERS [J].

LEGA, J ;

MOLONEY, JV ;

NEWELL, AC .

PHYSICAL REVIEW LETTERS, 1994, 73 (22) :2978-2981

← 1 2 →