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ASYMPTOTIC EQUIVALENCE OF ALMOST PERIODIC SOLUTIONS FOR A CLASS OF PERTURBED ALMOST PERIODIC SYSTEMS

Published online by Cambridge University Press:  25 August 2010

MANUEL PINTO ,
VICTOR TORRES  and
GONZALO ROBLEDO
MANUEL PINTO
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 7800024, Chile e-mail: pintoj@uchile.cl
VICTOR TORRES
Affiliation:
Departamento de Ciencias Físicas y Matemáticas, Universidad Arturo Prat, Avda. Arturo Prat 2120, Iquique 1110939, Chile e-mail: vtorres@unap.cl
GONZALO ROBLEDO
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 7800024, Chile e-mail: grobledo@uchile.cl
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Abstract

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The solutions of a perturbed linear ordinary differential equation (ODE) system are studied. Provided that some integrability and oddness conditions are satisfied, we show that they are asymptotically equivalent at t = ±∞ to the solutions of the unperturbed one. This fact is used to determine the existence of almost periodic or pseudo-almost periodic solutions of the perturbed system.

Keywords

34E1034C2734C41
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 583 - 592
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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