Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients

Abstract EN

This paper is dealt with the following system of difference equations xn+1=an/xn+bn/yn,yn+1=cn/xn+dn/yn, where n∈ℕ0=ℕ∪0, the initial values x0 and y0 are the positive real numbers, and the sequences ann≥0, bnn≥0, cnn≥0, and dnn≥0 are two-periodic and positive.

The system is an extension of a system where every positive solution is two-periodic or converges to a two-periodic solution.

Here, the long-term behavior of positive solutions of the system is examined by using a new method to solve the system.