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

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).


39A11 Stability of difference equations (MSC2000)
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