Some notes on ``Oscillatory and asymptotic behaviour of second order nonlinear difference equations''
\textit{X. He} [ibid. 175, No. 2, 482-498 (1993; Zbl 0780.39001)] asserted that if \(\{x_ n\}\) is a nontrivial solution of the second order nonlinear difference equation \(\Delta (r_ n \Delta x_ n) + f(n,x_ n) = 0\) such that \(x_ n f(n, x_ n) \leq 0\) for all \(n\) large, then \(\{x_ n\}\) must be nonoscillatory. One can easily see by means of counterexamples that this conclusion is wrong.
second order nonlinear difference equation
scientific article; zbMATH DE number 743900