Oscillation and nonoscillation of two-dimensional difference systems

This paper is concerned with the oscillation and nonoscillation behavior of solution of the nonlinear two-dimensional difference systemΔxn=ang(yn),Δxn=ang(yn),Δyn-1=-f(n,xn),n∈N(n0)={n0,n0+1,…}.Some necessary and sufficient conditions are given for the system to admit the existence of oscillatory and nonoscillatory solutions with special asymptotic properties. Some important results in the literatures are generalized. Examples to illustrate the result are included.