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

E. Thandapani; I.M. Arockiasamy

doi:10.4171/zaa/985

JournalszaaVol. 19, No. 3pp. 863–872

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

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Abstract

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

Δ a_{n} Δ (b_{n} Δ (c_{n} Δ y_{n})) + q_{n} f (y_{n + 1}) = h_{n} (n \in N_{0})

where $Δ$ is the forward difference operator $Δ y_{n} = y_{n + 1} - y_{n}, {a_{n}}, {b_{n}}, {c_{n}}, {q_{n}}, {h_{n}}$ 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