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

Abstract

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

ΔanΔ(bnΔ(cnΔyn))+qnf(yn+1)=hn(nN0)\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 Δ\Delta is the forward difference operator Δyn=yn+1yn,{an},{bn},{cn},{qn},{hn}\Delta y_n = y_{n+1} – y_n, \{a_n\}, \{b_n\}, \{c_n\}, \{q_n\}, \{h_n\} are real sequences, and ff is a real-valued continuous function. Also, sufficient conditions are provided which ensure that all non-oscillatory solutions of the equation approach zero as nn \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