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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: June 23, 2004
MathSciNet review: 2085163
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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: http://dx.doi.org/10.1090/S0002-9939-04-07520-3
PII: S 0002-9939(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