# Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations

### E. Thandapani

University of Madras, Chennai, India### I.M. Arockiasamy

Periyar University, Salem, India

## Abstract

Sufficient conditions are established for oscillation of all solutions of the fourth order difference equation

$\Delta a_n \Delta (b_n \Delta (c_n \Delta y_n)) + q_n f (y_{n+1}) = h_n \\ (n \in \mathbb N_0)$

where $\Delta$ is the forward difference operator $\Delta y_n = y_{n+1} – y_n, \{a_n\}, \{b_n\}, \{c_n\}, \{q_n\}, \{h_n\}$ are real sequences, and $f$ is a real-valued continuous function. Also, sufficient conditions are provided which ensure that all non-oscillatory solutions of the equation approach zero as $n \to \infty$. Examples are inserted to illustrate the results.

## Cite this article

E. Thandapani, I.M. Arockiasamy, Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations. Z. Anal. Anwend. 19 (2000), no. 3, pp. 863–872

DOI 10.4171/ZAA/985