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Oscillation and asymptotic behavior of two-dimensional difference systems. (English) Zbl 1148.39005

The authors investigate the oscillatory behavior of the solutions to a two-dimensional difference system \(\Delta x_n=b_ng(y_n)\), \(\Delta y_{n-1}=-a_nf(x_n),\) \(n\in N(n_0)=\{n_0,n_0+1, \dots\}\). Equivalent conditions for the oscillation of all solutions of the system are given, under some hypotheses.

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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References:

[1] Agarwal, R. P., Difference Equations and Inequalities (1992), Marcel Dekker: Marcel Dekker New York · Zbl 0784.33008
[2] Graef, J. R.; Thandapani, E., Oscillation of two-dimensional difference systems, Comput. Math. Appl., 38, 157-165 (1999) · Zbl 0964.39012
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