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Existence of nonoscillatory solutions of some higher order difference equations. (English) Zbl 1069.39010

The linear difference equation \[ \Delta^mx_n + \delta a_nx_{n+1} = 0 \] with \(m\geq 2\), \(\delta=\pm 1\), \(a_n>0\), \(\Delta x_n\) the forward difference and \(\Delta^m\) its iterate is considered. Nonoscillation conditions for the solutions are given; it is shown how to construct nonoscillatory unbounded solutions of the equation.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
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