On the existence of solutions for a class of fourth order differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Chapiro, Grigori¹  Faria, Luiz F. O.¹  Maldonado, Andre D.² 

[1] Univ Fed Juiz de Fora, Dept Matemat, BR-36036330 Juiz De Fora, MG, Brazil

[2] Univ Fed Itajuba, Inst Matemat & Computacao, BR-37500903 Itajuba, MG, Brazil

关键词: Extended Fisher-Kolmogorov equation;    Swift-Hohenberg equation;    Finite difference schemes;    Homoclinic solution;   

DOI  :  10.1016/j.jmaa.2015.01.012

来源: Elsevier

【 摘 要 】

We study the existence of the homoclinic solution of a class of nonlinear fourth order ordinary differential equations, which involve particular cases of the extended Fisher Kolmogorov and Swift-Hohenberg equations. We address the case when the source term possesses a nonlinear dependence on the first order derivative of the solution. The main result follows from an iterative method using the sequence of solutions obtained through the mountain-pass technique. In order to illustrate this method some numerical examples are shown. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free