Proceedings of the American Mathematical Society

Author(s): Anatoliy Samoilenko; Manuel Pinto; Sergei Trofimchuk
Journal: Proc. Amer. Math. Soc. 133 (2005), 145-154.
MSC (2000): Primary 34E05
Posted: June 23, 2004
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34E05

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: 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
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society

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