On solutions of a system of rational difference equations
Yu Yang, Li Chen and Yong-Guo Shi
Received: February 10, 2009; Accepted: September 25, 2010
Abstract. In this paper we investigate the system of rational difference equations
where q is a positive integer with p < q, p \not | q, p is an odd number and p ³ 3, both a and b are nonzero real constants and the initial values x-q+1, x-q+2, . . . x0, y-q+1, y-q+2, . . ., y0 are nonzero real numbers. We show all real solutions of the system are eventually periodic with period 2pq (resp. 4pq) when (a/b)q = 1 (resp. (a/b)q = -1), characterize the asymptotic behavior of the solutions when a ³ b, which generalizes Őzban's results of in [Appl. Math. Comput. 188 (2007), 833-837].
Keywords: System of difference equations; homogeneous equations of degree one; eventually periodic solutions.
AMS Subject classification: Primary: 39A11, 37B20.
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