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Oscillation theorems for certain second order nonlinear difference equations. (English) Zbl 0874.39012

Discrete inequalities are used to obtain sufficient conditions for the oscillation of all solutions of the difference equation \[ \Delta(a_n(\Delta y_n)^\sigma)+q_{n+1} f(y_{n+1})=r_n,\quad n\geq 0 \] where \(0<\sigma=p/q\) with \(p\), \(q\) odd integers, or \(p\) even and \(q\) odd integer. The results obtained here generalize some of the results of J. W. Hooker and W. T. Patula [J. Math. Anal. Appl. 91, 9-29 (1983; Zbl 0508.39005)] and E. Thandapani, I. Györi and B. S. Lalli [J. Math. Anal. Appl. 186, No. 1, 200-208 (1994; Zbl 0823.39004)].

MSC:

39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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