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 Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 380568 19 pages doi 2009 380568 Research Article Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional Difference Equations in Phase Spaces Claudio Vidal Departamento de Matemdtica Facultad de Ciencias Universidad del Bio Bio Casilla 5-C Concepción Chile Correspondence should be addressed to Claudio Vidal clvidal@ Received 20 November 2008 Revised 23 March 2009 Accepted 10 June 2009 Recommended by Donal O Regan The existence of periodic almost periodic and asymptotically almost periodic of periodic and almost periodic of abstract retarded functional difference equations in phase spaces is obtained by using stability properties of a bounded solution. Copyright 2009 Claudio Vidal. 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 the existence of periodic almost periodic and asymptotic almost periodic solutions of the following functional difference equations with infinite delay x n 1 F n xn n n0 0 assuming that this system possesses a bounded solution with some property of stability. In F N n0 B Cr and B denotes an abstract phase space which we will define later. The abstract space was introduced by Hale and Kato 1 to study qualitative theory of functional differential equations with unbounded delay. There exists a lot of literature devoted to this subject we refer the reader to Corduneanu and Lakshmikantham 2 Hino et al. 3 . The theory of abstract retarded functional difference equations in phase space has attracted the attention of several authors in recent years. We only mention here Murakami 4 5 Elaydi et al. 6 Cuevas and Pinto 7 8 Cuevas and Vidal 9 and Cuevas and Del Campo 10 . 2 Advances in Difference Equations As usual we
