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

### E. Thandapani

University of Madras, Chennai, India### S. Pandian

Periyar University, Salem, India

## Abstract

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 $n \in \mathbb N_0$.

## Cite this article

E. Thandapani, S. Pandian, On the Oscillatory Behaviour of Solutions of Second Order Nonlinear Difference Equations. Z. Anal. Anwend. 13 (1994), no. 2, pp. 347–358

DOI 10.4171/ZAA/509