Nonoscillatory solutions of a second-order nonlinear discrete system

A complete characterization for nonoscillatory solutions of a coupled nonlinear difference system is presented. Nonoscillatory solutions are classified into several classes according to their limit behavior, and necessary and sufficient conditions for the existence in each of these classes are established. The multiplicity of solutions is also examined and explicit asymptotic formulas are derived. Possible generalizations and comparisons of our results with existing ones are discussed as well.