Báo cáo hóa học: "Research Article On the Recursive Sequence xn"

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 On the Recursive Sequence xn | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 327649 11 pages doi 2009 327649 Research Article On the Recursive Sequence xn 1 A jp_1 xn C. J. Schinas G. Papaschinopoulos and G. Stefanidou School of Engineering Democritus University of Thrace 67100 Xanthi Greece Correspondence should be addressed to G. Papaschinopoulos gpapas@ Received 11 June 2009 Revised 10 September 2009 Accepted 21 September 2009 Recommended by Agacik Zafer In this paper we study the boundedness the persistence the attractivity and the stability of the positive solutions of the nonlinear difference equation xn 1 a x n_x xf n 0 1 . where a p q e 0 to and x_1 x0 e 0 to . Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution. Copyright 2009 C. J. Schinas 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 Difference equations have been applied in several mathematical models in biology economics genetics population dynamics and so forth. For this reason there exists an increasing interest in studying difference equations see 1-28 and the references cited therein . The investigation of positive solutions of the following equation Xn A A Y xn-m n 0 1 . where A p q e 0 to and k m e N k fm was proposed by Stevic at numerous conferences. For some results in the area see for example 3-5 8 11 12 19 22 24 25 28 . In 22 the author studied the boundedness the global attractivity the oscillatory behavior and the periodicity of the positive solutions of the equation V X Xn-1 Xn 1 a p x. xn n 0 1 . 2 Advances in Difference Equations where a p are positive constants and the initial conditions x-1 x0 are positive numbers see also 5 for more results on this equation . .

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