tailieunhanh - Báo cáo hóa học: " Research Article On the Solutions of Systems 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 On the Solutions of Systems of Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 143943 9 pages doi 2008 143943 Research Article On the Solutions of Systems of Difference Equations Ibrahim Yalcinkaya Cengiz Cinar and Muhammet Atalay Mathematics Department Faculty of Education Selcuk University 42099 Konya Turkey Correspondence should be addressed to Ibrahim Yalcinkaya iyalcinkaya1708@ Received 19 March 2008 Accepted 19 May 2008 Recommended by Bing Zhang We show that every solution of the following system of difference equations x A x 2 x 2 - 1 x 2 x 3 x3 - 1 .JD x 1 x 1 - 1 as well as of the svstem x 1 xx .xx - 1k x 2 Xn 1 xn xn xn 1 xn xn as we as oi te syslem xn 1 xn xn xn 1 xip xip 1 x k x. k 1 x. k 1 1 is eriodic with eriod 2k if k 0 mod2i. and with xn yxn xn 1 xn Ixn .1y J-s pel w in I _per iod. Jv 11- J XJ yii iod -y ai Id. w Hl I Dprind k it k 0 mod 7 whpfp thp initial valiiPR am finnzpfn mal niirnhpfR tor V 1P v 2 vik 1 per io HLv were e 1 la v mc are Iiv-Iizer o te i 11 Hiners or 0 0 0 . Copyright 2008 Ibrahim Yalcinkaya 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 appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations having applications in biology ecology economy physics and so on 1 . So recently there has been an increasing interest in the study of qualitative analysis of rational difference equations and systems of difference equations. Although difference equations are very simple in form it is extremely difficult to understand thoroughly the behaviors of their solutions. see 1-12 and the references cited therein. Papaschinopoulos and Schinas 9 10 studied the behavior of the positive solutions of the system of two Lyness difference equations .-by c _ dxn e