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 {yny_n} of a difference equation of the form Δ(anΔyn)+qn+1f(yn+1=rn(nN0;an,qn,rnCR;f:RR)\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 infnyn=0_{n \to \infty} |y_n| = 0. Also two other results are established for all solutions of this equation to be oscillatory when rn=0r_n = 0 for all nN0n \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