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Báo cáo hóa học: " Research Article Almost Automorphic Solutions of Difference Equations"

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 Almost Automorphic Solutions of Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 59i380 15 pages doi 10.1155 2009 591380 Research Article Almost Automorphic Solutions of Difference Equations Daniela Araya Rodrigo Castro and Carlos Lizama Departamento de Matemdtica Universidad de Santiago 9160000 Santiago Chile Correspondence should be addressed to Carlos Lizama carlos.lizama@usach.cl Received 25 March 2009 Accepted 13 May 2009 Recommended by Mouffak Benchohra We study discrete almost automorphic functions sequences defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f n we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Au n Tu n f n . We also prove the existence of a discrete almost automorphic solution of the nonlinear difference equation Au n Tu n g n u n assuming that g n x is discrete almost automorphic in n for each x e X satisfies a global Lipschitz type condition and takes values on X . Copyright 2009 Daniela Araya et al. 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 The theory of difference equations has grown at an accelerated pace in the last decades. It now occupies a central position in applicable analysis and plays an important role in mathematics as a whole. A very important aspect of the qualitative study of the solutions of difference equations is their periodicity. Periodic difference equations and systems have been treated among others by Agarwal and Popenda 1 Corduneanu 2 Halanay 3 Pang and Agarwal 4 Sugiyama 5 Elaydi 6 and Agarwal 7 . Almost periodicity of a discrete function was first introduced by Walther 8 9 and then by Corduneanu 2 . Recently several papers 10-16 are devoted to study existence of .