Abstract :
Certain almost periodic forced perturbed systems with piecewise argument are considered in this paper.
By using the contraction mapping principle and some new analysis technique, some sufficient conditions
are obtained for the existence and uniqueness of almost periodic solution of these systems. Furthermore,
we study the harmonic and subharmonic solutions of these systems. The obtained results generalize the
previous known results such as [A.M. Fink, Almost Periodic Differential Equation, Lecture Notes in Math.,
vol. 377, Springer-Verlag, Berlin, 1974; C.Y. He, Almost Periodic Differential Equations, Higher Education
Press, Beijing, 1992 (in Chinese); Z.S. Lin, The existence of almost periodic solution of linear system,
Acta Math. Sinica 22 (5) (1979) 515–528 (in Chinese); C.Y. He, Existence of almost periodic solutions
of perturbation systems, Ann. Differential Equations 9 (2) (1992) 173–181; Y.H. Xia, M. Lin, J. Cao, The
existence of almost periodic solutions of certain perturbation system, J. Math. Anal. Appl. 310 (1) (2005)
81–96]. Finally, a tangible example and its numeric simulations show the feasibility of our results, the
comparison between non-perturbed system and perturbed system, the relation between systems with and
without piecewise argument.
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