The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (203 KB) | Metadata | Table of Contents | ZAA summary
Volume 19, Issue 3, 2000, pp. 863–872
DOI: 10.4171/ZAA/985

Published online: 2000-09-30

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

E. Thandapani[1] and I.M. Arockiasamy[2]

(1) University of Madras, Chennai, India
(2) Periyar University, Salem, India

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.

Keywords: Fourth order difference equations, oscillation, non-oscillation

Thandapani E., Arockiasamy I.M.: Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations. Z. Anal. Anwend. 19 (2000), 863-872. doi: 10.4171/ZAA/985