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Asymptotic behavior of nonlinear difference systems. (English) Zbl 1030.39004

The authors consider the system \[ \Delta x_{n} = a_{n}f(y_{n}),\qquad \Delta y_{n-1} = b_{n}g(x_{n}) \] under the following conditions: a) for some \(n_{0}>0\), \(a_{n}>0\) provided \(n\geq n_{0}\); b) \(f\) and \(g\) increasing with \(xf(x)>0\), \(xg(x)>0\). The following topics are considered: non-oscillation, monotonicity and asymptotic behavior of positive solutions.

MSC:

39A11 Stability of difference equations (MSC2000)
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