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On a nonlinear second order system of difference equations
Journal article   Peer reviewed

On a nonlinear second order system of difference equations

Stevo Stević, Mohammed A. Alghamdi, Abdullah Alotaibi and Naseer Shahzad
Applied mathematics and computation, Vol.219(24), pp.11388-11394
15/08/2013
DOI: https://doi.org/10.1016/j.amc.2013.05.015

Abstract

Boundedness character Second order System of difference equations
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.

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