Stability and Entering of the Origin for Real, Nonlinear, Autonomous Differential Equations of Third Order

This paper is concerned with the asymptotic behavior of solutions to third order differential equations in the neighborhood of a stable critical point. In particular, the question of whether or not solution trajectories enter the critical point is investigated. Two new theorems on entering (extensio...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on mathematical analysis 1971-02, Vol.2 (1), p.133-148
Main Authors: Roberts, Charles E., Belford, Geneva G.
Format: Article
Language:English
Subjects:
Theorems
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is concerned with the asymptotic behavior of solutions to third order differential equations in the neighborhood of a stable critical point. In particular, the question of whether or not solution trajectories enter the critical point is investigated. Two new theorems on entering (extensions of known theorems for the two-dimensional case) are proved, and these, as well as known results on asymptotic behavior, are applied to a case-by-case analysis of the possibilities for third order equations.
ISSN:0036-1410
1095-7154
DOI:10.1137/0502012