The existence of almost periodic solutions of certain perturbation systems

AbstractCertain almost periodic perturbation systems are considered in this paper. By using the roughness theory of exponential dichotomies and the contraction mapping principle, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of the above systems. Our results generalize those in [J.K. Hale, Ordinary Differential Equations, Krieger, Huntington, 1980; C. He, Existence of almost periodic solutions of perturbation systems, Ann. Differential Equations 9 (1992) 173–181; M. Lin, The existence of almost periodic solution and bounded solution of perturbation systems, Acta Math. Sinica 22A (2002) 61–70 (in Chinese); W.A. Coppel, Almost periodic properties of ordinary differential equations, Ann. Math. Pura Appl. 76 (1967) 27–50; A.M. Fink, Almost Periodic Differential Equations, Lecture Notes in Math., vol. 377, Springer-Verlag, New York, 1974; Y. Xia, F. Chen, A. Chen, J. Cao, Existence and global attractivity of an almost periodic ecological model, Appl. Math. Comput. 157 (2004) 449–475]