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Generalized discrete Riccati equation and oscillation of half-linear difference equations. (English) Zbl 1038.39002
Summary: Oscillation criteria for the second-order half-linear difference equation \[ \Delta\bigl( r_k|\Delta y_k|^{\alpha-1} \text{sgn}\,\Delta y_k \bigr)+p_k| y_{k+1}|^{\alpha-1} \text{sgn}\;y_{k+1}=0, \quad\alpha<1, \] to be oscillatory are obtained. These criteria are proved using the Riccati technique.

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