KrylovBogolyubov averaging of asymptotically autonomous differential equations
Authors:
Anatoliy Samoilenko, Manuel Pinto and Sergei Trofimchuk
Journal:
Proc. Amer. Math. Soc. 133 (2005), 145154
MSC (2000):
Primary 34E05
Published electronically:
June 23, 2004
MathSciNet review:
2085163
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasiperiodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous VanderPol 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/S0002993904075203
PII:
S 00029939(04)075203
Keywords:
Asymptotic integration,
asymptotically autonomous equation,
Levinson theorem,
KrylovBogolyubov averaging principle,
VanderPol 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
