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Oscillation of third-order difference equations. (English) Zbl 1069.39015

The author considers the third order difference equation \[ \Delta^3V_n+P_nV_{n+1}=0, \quad n\geq n_0,\tag{1} \] where \(P_n>0\) for \(n\geq n_0\) and \(\Delta\) denotes the difference operator \(\Delta V_n=V_{n+1}-V_n\) for any sequence \(\{V_n\}\) of real numbers. Using the Riccati transformation techniques, new conditions which are sufficient for all solutions of (1) to be oscillatory or tend to zero as \(n\to \infty\), are established.

MSC:

39A11 Stability of difference equations (MSC2000)
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