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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay | Hindawi Publishing Corporation Advances in Difference Equations Volume 2007 Article ID 68023 15 pages doi 10.1155 2007 68023 Research Article Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay Yihong Song Received 4 November 2006 Revised 29 January 2007 Accepted 29 January 2007 Recommended by John R. Graef For periodic and almost periodic functional difference equations with finite delay the existence of periodic and almost periodic solutions is obtained by using stability properties of a bounded solution. Copyright 2007 Yihong Song. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In this paper we study periodic and almost periodic solutions of the following functional difference equations with finite delay x n 1 F n xn n 0 1.1 under certain conditions for F n see below where n j and T are integers andxn will denote the function x n j j T T 1 . 0. Equation 1.1 can be regarded as the discrete analogue of the following functional differential equation with bounded delay dx dt t xt t 0 xt 0 x t 0 ộ t -Ơ t 0. 1.2 Almost periodic solutions of 1.2 have been discussed in 1 . The aim of this paper is to extend results in 1 to 1.1 . Delay difference equations or functional difference equations no matter with finite or infinite delay inspired by the development of the study of delay differential equations have been studied extensively in the past few decades see 2-11 to mention a few and 2 Advances in Difference Equations references therein . Recently several papers 12-17 are devoted to study almost periodic solutions of difference equations. To the best of our knowledge little work has been done on almost periodic solutions of nonlinear functional difference equations with finite delay via uniform stability properties of a bounded solution. This motivates us
