## 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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