Differential and Integral Equations

On the partial asymptotic stability in nonautonomous differential equations

Oleksiy Ignatyev

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

A system of ordinary differential equations $dx/dt=X(t,x)$ which has a zero solution $x=0$ is considered. It is assumed that there exists a function $V(t,x)$, positive definite with respect to part of state variables such that its derivative $dV/dt$ is nonpositive. It is proved that if the function $\sum_{i=1}^jV_i^2$ is positive definite with respect to part of the studying variables, then the zero solution is asymptotically stable with respect to these variables. Here $V_1=dV/dt, V_{i}=dV_{i-1}/dt, \quad i=2, \dots,j;\quad j$ is some positive integer. The instability criterion is also obtained.

Article information

Source
Differential Integral Equations, Volume 19, Number 7 (2006), 831-839.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050352

Mathematical Reviews number (MathSciNet)
MR2235897

Zentralblatt MATH identifier
1212.34154

Subjects
Primary: 34D20: Stability

Citation

Ignatyev, Oleksiy. On the partial asymptotic stability in nonautonomous differential equations. Differential Integral Equations 19 (2006), no. 7, 831--839. https://projecteuclid.org/euclid.die/1356050352


Export citation