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Glasgow Mathematical Journal (1)

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ASYMPTOTIC EQUIVALENCE OF ALMOST PERIODIC SOLUTIONS FOR A CLASS OF PERTURBED ALMOST PERIODIC SYSTEMS
MANUEL PINTO, VICTOR TORRES, GONZALO ROBLEDO
Journal:

Glasgow Mathematical Journal / Volume 52 / Issue 3 / September 2010

Published online by Cambridge University Press:

25 August 2010, pp. 583-592

Print publication:

September 2010
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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.