Oscillation of two-dimensional difference systems

The authors consider the nonlinear two-dimensional difference system Δxn=bng(yn), Δyn−1=−anf(xn, εN(no={no,no+1…}, where n0 ε N = 1, 2, …, an and bn, n ε N (n0), are real sequences, and f, g : R → R are continuous with uf(u) > 0 and ug(u) > 0 for u ≠ 0. A solution (xn, yn) of the system is oscillatory if both components are oscillatory. The authors obtain sufficient conditions for all solutions of the system to be oscillatory. Some of their results allow an to oscillate. Examples to illustrate the results are included.