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author:

Xia, Y. (Xia, Y..) [1] | Huang, Z. (Huang, Z..) [2] | Han, M. (Han, M..) [3]

Indexed by:

Scopus

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. © 2006 Elsevier Inc. All rights reserved.

Keyword:

Almost periodic solution; Contraction mapping; Exponential dichotomy

Community:

  • [ 1 ] [Xia, Y.]The Institute of Mathematics, Shanghai Normal University, Shanghai, 200234, China
  • [ 2 ] [Xia, Y.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
  • [ 3 ] [Huang, Z.]School of Sciences, Jimei University, Xiamen, Fujian 361021, China
  • [ 4 ] [Han, M.]The Institute of Mathematics, Shanghai Normal University, Shanghai, 200234, China

Reprint 's Address:

  • [Xia, Y.]The Institute of Mathematics, Shanghai Normal University, Shanghai, 200234, China

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Source :

Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Year: 2007

Issue: 2

Volume: 333

Page: 798-816

0 . 8 7 2

JCR@2007

1 . 2 0 0

JCR@2023

JCR Journal Grade:1

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 27

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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