Oscillation and comparison theorems for half-linear second-order difference equations. (English) Zbl 0983.39006

Thandapani, E.; Ravi, K.; Graef, J. R.

Comput. Math. Appl. 42, No. 6-7, 953-960 (2001).

Authors’ abstract: The authors consider second-order difference equations of the type \[ \Delta\bigl((\Delta y_n)^\alpha \bigr)+ q_ny^\alpha_{ \sigma (n)}=0, \tag{E} \] where \(\alpha>0\) is the ratio of odd positive integers, \(\{q_n\}\) is a positive sequence, and \(\{\sigma(n)\}\) is a positive increasing sequence of integers with \(\sigma(n) \to\infty\) as \(n\to\infty\). They give some oscillation and comparison results for equation (E).

Reviewer: Sui Sun Cheng (Hsinchu)

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

half-linear second-order difference equations; oscillation; comparison

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