Asymptotic behavior of the solution to a differential equation with a small parameter when the stability lines of the limit solution intersect

被引：1

作者：

Dolbeeva, S. F. ^{[1
]}

Il'in, A. M. ^{[1
]}

机构：

[1] Chelyabinsk State Univ, Chelyabinsk 454021, Russia

来源：

DOKLADY MATHEMATICS | 2006年 / 73卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Asymptotic behavior - Limit solution intersects - Small parameters - Stability lines;

D O I：

10.1134/S1064562406030197

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The asymptotic behavior of the solution to a differential equation with a small parameter when the stability lines of the limit solution intersect, is discussed. The initial value problems for systems of ordinary differential equations with a small parameter multiplying the derivatives are analyzed. The stability is lost and the asymptotic behavior is rather complex at the intersection points of the graphs. One of the simplest cases of asymptotic behavior is when the limit equation has one or several stable solutions.

引用

页码：388 / 390

页数：3