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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 13, Issue 2, 1994, pp. 347–358**

**DOI: 10.4171/ZAA/509**

Published online: 1994-06-30

On the Oscillatory Behaviour of Solutions of Second Order Nonlinear Difference Equations

E. Thandapani^{[1]}and S. Pandian

^{[2]}(1) University of Madras, Chennai, India

(2) Periyar University, Salem, India

By using simple discrete inqualities sufficient conditions are provided for the solution {$y_n$} of a difference equation of the form $\Delta(a_n \Delta y_n) + q_{n+1} f (y_{n+1} = r_n (n \in \mathbb N_0; {a_n}, {q_n}, {r_n} C \mathbb R; f : \mathbb R \to \mathbb R)$ to be oscillatory or to satisfy lim inf$_{n \to \infty} |y_n| = 0$. Also two other results are established for all solutions of this equation to be oscillatory when $r_n = 0$ for all $n \in \mathbb N_0$.

*Keywords: *Second order nonlinear difference equations, oscillation

Thandapani E., Pandian S.: On the Oscillatory Behaviour of Solutions of Second Order Nonlinear Difference Equations. *Z. Anal. Anwend.* 13 (1994), 347-358. doi: 10.4171/ZAA/509