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

Wong, Patricia J. Y.; Agarwal, Ravi P.

J. Math. Anal. Appl. 204, No. 3, 813-829 (1996).

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)].

Reviewer: E.Thandapani (Salem)

MSC:

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

Keywords:

second order nonlinear difference equations; oscillation

Citations:

Zbl 0508.39005; Zbl 0823.39004