Melnikov method for discontinuous planar systems

被引：63

作者：

Kukucka, Peter

机构：

[1] Karpatská 3

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 66卷 / 12期

关键词：

homoclinic solution; non-smooth Melnikov function; discontinuous system;

D O I：

10.1016/j.na.2006.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper treats the. occurrence of homoclinic solutions in planar systems with discontinuous right-hand side. More precisely, we deal with a T-periodic perturbed system such that the unperturbed system is an autonomous possessing homoclinic orbit. By means of the so-called "non-smooth" Melnikov function there is shown the existence of a homoclinic solution for a perturbed system. The non-smooth Melnikov function is derived, and the method of how to find it in concrete problems is also introduced. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：2698 / 2719

页数：22