Krylov-Bogolyubov averaging of asymptotically autonomous differential equations

Authors:
Anatoliy Samoilenko, Manuel Pinto and Sergei Trofimchuk

Journal:
Proc. Amer. Math. Soc. **133** (2005), 145-154

MSC (2000):
Primary 34E05

DOI:
https://doi.org/10.1090/S0002-9939-04-07520-3

Published electronically:
June 23, 2004

MathSciNet review:
2085163

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Abstract | References | Similar Articles | Additional Information

Abstract: We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasi-periodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous Van-der-Pol oscillator.

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Additional Information

**Anatoliy Samoilenko**

Affiliation:
Institute of Mathematics, National Academy of Sciences, Tereshchenkyvs’ka str., 3, Kiev, 252601, Ukraine

Email:
sam@imath.kiev.ua

**Manuel Pinto**

Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

Email:
pintoj@uchile.cl

**Sergei Trofimchuk**

Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

Address at time of publication:
Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

Email:
trofimch@uchile.cl

DOI:
https://doi.org/10.1090/S0002-9939-04-07520-3

Keywords:
Asymptotic integration,
asymptotically autonomous equation,
Levinson theorem,
Krylov-Bogolyubov averaging principle,
Van-der-Pol oscillator,
adiabatic oscillator

Received by editor(s):
May 7, 2002

Received by editor(s) in revised form:
September 9, 2003

Published electronically:
June 23, 2004

Additional Notes:
The first author was supported in part by FONDECYT (Chile), project 7960723

The second and third authors were supported in part by FONDECYT (Chile), project 8990013

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2004
American Mathematical Society