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Classification schemes for nonoscillatory solutions of two-dimensional nonlinear difference systems. (English) Zbl 1006.39013

Classification schemes for nonoscillatory solutions of a class of two-dimensional nonlinear difference systems of the form \[ \Delta x_{n}=a_{n}f(y_{n}),\qquad \Delta y_{n}=-b_{n}g(x_{n}) \] are given in terms of their asymptotic magnitudes. Necessary, sufficient and necessary and sufficient conditions for the existence of these solutions are also established.

MSC:

39A11 Stability of difference equations (MSC2000)
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