On a nonlinear second order system of difference equations

Abstract

We prove that all positive solutions of the next system of difference equationsxn+1=A+ynpxn-1q,yn+1=A+xnpyn-1q,n N0,where parameters A,p and q are positive numbers, are bounded if one of the following conditions is satisfied p2<4q, or 2q≤p<1+q,q(0,1), and that the system has positive unbounded solutions when p2≥4q>4, or p≥1+q, q≤1, completely describing the boundedness character of the system in this case.