Note on ''Oscillation theorems for certain second order nonlinear difference equations'' (Q1270914)

The aim of the note, which concerns the paper of \textit{P. J. Y. Wong}, and \textit{R. P. Agarwal} [ibid. 204, No. 3, 813-829 (1996; Zbl 0874.39012)], is to obtain some oscillation theorems for the equation \[ \Delta\bigl(a_{n-1}|\Delta y_{n-1}|^{\alpha-1}\Delta y_{n-1}\bigr)+q_nf(y_n)=r_n,\quad n\geq 1, \] where \(\alpha>0\), \(\{a_n\}\) is an eventually positive real sequence, \(\{q_n\}\) and \(\{r_n\}\) are real sequences, and \(f:\mathbb{R}\to \mathbb{R}\) is continuous and nondecreasing with \(uf(u)>0\) for \(u\neq 0\). A nontrivial real sequence \(\{y_n\}\), \(n\geq 0\), is called a solution of \((E)\) if \(\{y_n\}\) satisfies equation \((E)\) for all \(n\geq 0\). A solution \(\{y_n\}\) is said to be oscillatory if it is neither eventually positive nor negative, and nonoscillatory otherwise.