Nonresonance Conditions for the Existence of Almost Periodic Solutions of Almost Periodic Systems

1971 ◽  
Vol 21 (2) ◽  
pp. 362-366 ◽  
Author(s):  
A. M. Fink ◽  
G. Seifert
Keyword(s):  
Periodic Solutions ◽  
Periodic Systems ◽  
Almost Periodic Solutions ◽  
Almost Periodic

scholarly journals On linear almost periodic systems with bounded solutions

1997 ◽  
Vol 55 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. I. Tkachenko
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Linear Differential Equations ◽  
Periodic Systems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Bounded Solutions ◽  
Adjoint Matrix ◽  
Frequency Module ◽  
Linear Differential

It is proved that in every neighbourhood of a system of linear differential equations with almost periodic skew-adjoint matrix with frequency module ℱ there exists a system with frequency module contained in the rational hull of ℱ possessing all almost periodic solutions.

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

2010 ◽  
Vol 52 (3) ◽  
pp. 583-592 ◽  
Author(s):  
MANUEL PINTO ◽  
VICTOR TORRES ◽  
GONZALO ROBLEDO
Keyword(s):  
Periodic Solutions ◽  
Linear Ordinary Differential Equation ◽  
Periodic Systems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Asymptotic Equivalence ◽  
Perturbed System ◽  
Pseudo Almost Periodic Solutions ◽  
Ode System ◽  
Pseudo Almost Periodic

AbstractThe 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.

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