Some notes on “Oscillatory and asymptotic behaviour of second order nonlinear difference equations”. (English) Zbl 0816.39001

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.


39A10 Additive difference equations


Zbl 0780.39001
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