ON A SOLVABLE SYSTEM OF DIFFERENCE EQUATIONS OF HIGHER-ORDER WITH PERIOD TWO COEFFICIENTS

Abstract

We show that the next di§erence equations system xn+1 = anxnk+1ynk yn n + n+1; yn+1 = bnynk+1xnk xn n + n+1; n 2 N0; where N0 = N [ f0g, the sequences (an)n2N0 , (bn)n2N0 , ( n)n2N0 , (n)n2N0 are two periodic and the initial conditions xi, yi i 2 f0; 1; : : : ; kg, are nonzero real numbers, can be solved. Also, we investigate the behavior of solutions of above mentioned system when a0 = b1 and a1=ba.