Oscillation for Certain Third Order Functional Delay Difference Equation


Affiliations

  • Government Arts College, Department of Mathematics, Udumalpet, Tamilnadu, 642 126, India

Abstract

This paper is concerned with the third order functional delay difference equation of the form Δ(CnΔ(anΔxn)) + mΣi=1pniΔxσi(n-r) + mΣi=1qnif (xσi(n-r)) = 0. We obtain some new oscillation criteria by using Riccati transformation technique. Examples are given to illustrate the results.

Keywords

Difference equation, Delay, Oscillation, Nonoscillation, Riccati transformation

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References

R. P. Agarwal, M. Bohner, S. R. Grace and D. O'Regen, Discrete Oscillation Theory, Hindawi Publishing corporation, New York, 2005.

R. P. Agarwal, Difference Equations and Inqualities, Theory, Methods and Applications, Second Edition, Marcel Dekker, New York, 2000.

S. R. Grace and B. S. Lalli, Oscillation theorems for forced neutral difference equations, J. Math., Anal. Appl., 187 (1994), 91 - 106.

J. Graef and E. Thandapani, Oscillatory and asymptotic behavior of solutions of third order delay difference equations, Funk. Ekvac., 42 (1999) 355 - 369.

W. G. Kelley, A. C. Peterson, Difference Equations; An Introduction with Applications. New York. Acdemic Press (1991).

H. J. Li and C. C. Yeh, Oscillation criteria for second-order neutral delay difference equations, Advances in difference equations, II. Comput. Math. Appl., 36 (1998), 123 - 132.

R. Savithri and E. Thandapani, Oscillatory properties of third order neutral delay dif- ferential equations, Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 27, (2002), 342 - 350.

S. H. Saker, Oscillation and asymptotic behaviour of third-order nonlinear neutral delay di erence equations, Dynam. Systems Appl., 15 (2006), 549 - 567.

S. H. Saker, Oscillation criteria of third-order nonlinear delay differential equations, Math. Slovaca., 56 (2006), 433 - 450.

B. Smith and Jr. W. E. Taylor, Nonlinear third order di erence equations: Oscillatory and asymptotic behaviour, Tamakang J. Math., 19 (1988), 91 - 95.

B. Selvaraj and I. Mohammed Ali Ja er, Oscillation theorems of solutions for certain third order functional difference equations with delay, Bull. Pure and Applied Sc., 29(2) (2010), 207 - 216.

B. Selvaraj and I. Mohammed Ali Jaffer, Oscillation behavior of certain fourth order linear and nonlinear difference equations, Adv. Theoretial Appl. Math., 6(2), (2011), 203 - 211.

B. Selvaraj and I. Mohammed Ali Ja er, On the oscillation of the solution to third order difference equations, J. Computer Math. Sci., 1(17), (2010), 873 - 876.

A. Tiryaki and M. F. Aktas, Oscillation criteria of a certain class of third order non- linear delay differential equations with damping, J. Math. Anal. Appl., 325 (2007), 54 - 68.

Yadaiah Arupula and V. Dharmaiah, Oscillation of Third-order Nonlinear Delay Difference Equation, Int. J. Math. and Appl., 6(3) (2018) 181 - 191.


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