Oscillation theorems for certain second order nonlinear difference equations
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 \textit{J. W. Hooker} and \textit{W. T. Patula} [J. Math. Anal. Appl. 91, 9-29 (1983; Zbl 0508.39005)] and \textit{E. Thandapani, I. Györi} and \textit{B. S. Lalli} [J. Math. Anal. Appl. 186, No. 1, 200-208 (1994; Zbl 0823.39004)].
second order nonlinear difference equations
scientific article; zbMATH DE number 1005601