Differential and Integral Equations

Stable periodic solutions of perturbed autonomous equations in one critical case

I. Fomenko and H. I. Freedman

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Abstract

We consider an autonomous perturbation of an autonomous system of ordinary differential equations, when a periodic solution of the autonomous system has a nontrivial multiplier equal to $1$ or $-1$. We derive criteria for the perturbed system to have an orbitally asymptotically stable periodic solution using a technique of stable fixed points of monotone operators together with a bifurcation technique due to M.A. Krasnoselskii.

Article information

Source
Differential Integral Equations, Volume 8, Number 5 (1995), 1135-1143.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056047

Mathematical Reviews number (MathSciNet)
MR1325549

Zentralblatt MATH identifier
0822.34046

Subjects
Primary: 34C25: Periodic solutions
Secondary: 34D20: Stability 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47H15 47N20: Applications to differential and integral equations

Citation

Fomenko, I.; Freedman, H. I. Stable periodic solutions of perturbed autonomous equations in one critical case. Differential Integral Equations 8 (1995), no. 5, 1135--1143. https://projecteuclid.org/euclid.die/1369056047


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