Oscillation of certain second order nonlinear difference equations (Q1916861)

The authors establish some new sufficient conditions for the oscillation of all solutions of the difference equation \(\Delta^2 y_{n - 1} + q_n f(y_n) = 0\), \(n = 1, 2, \dots\) where \(f : \mathbb{R} \to \mathbb{R}\) is continuous and nondecreasing with \(uf (u) > 0\) for \(u \neq 0\) and \(\{q_n\}\) is a real sequence. For related results see the papers of \textit{E. Thandapani}, \textit{I. Györi} and \textit{B. S. Lalli} [J. Math. Anal. Appl. 186, No. 1, 200-208 (1994; Zbl 0823.39004)] and of \textit{E. Thandapani} and \textit{S. Pandian} [Z. Anal. Anwend. 13, No. 2, 347-358 (1994; Zbl 0803.39004)].