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 Dynamics for Nonlinear Difference Equation p xn 1 αxn−k / β γxn−l | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 235691 13 pages doi 2009 235691 Research Article Dynamics for Nonlinear Difference Equation Xn 1 axn-k fi ỴX Dongmei Chen 1 Xianyi Li 1 and Yanqin Wang2 1 College of Mathematics and Computational Science Shenzhen University Shenzhen Guangdong 518060 China 2 School of Physics Mathematics Jiangsu Polytechnic University Changzhou 213164 Jiangsu China Correspondence should be addressed to Xianyi Li xyli@ Received 19 April 2009 Revised 19 August 2009 Accepted 9 October 2009 Recommended by Mariella Cecchi We mainly study the global behavior of the nonlinear difference equation in the title that is the global asymptotical stability of zero equilibrium the existence of unbounded solutions the existence of period two solutions the existence of oscillatory solutions the existence and asymptotic behavior of non-oscillatory solutions of the equation. Our results extend and generalize the known ones. Copyright 2009 Dongmei Chen 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 Consider the following higher order difference equation axn-k xn 1 p n 0 1 p YXn-l where k l e 0 1 2 the parameters a p Y and p are nonnegative real numbers and the initial conditions x_ max k I x_1 and x0 are nonnegative real numbers such that p YxP-1 0 Yn 0- It is easy to see that if one of the parameters a Y p is zero then the equation is linear. If p 0 then can be reduced to a linear one by the change of variables xn eyn. So in the sequel we always assume that the parameters a p Y and p are positive real numbers. 2 Advances in Difference Equations The change of variables xn fl p 1 pyn reduces into the following equation . - ryn-k 1 yn 1 1 p n 0 1 . yn-l where r a p 0. Note that y1 0 is always an .