Oscillation theorems for second order neutral difference equations with “Maxima”

S.Rajan; K.Malathi

doi:10.26637/MJM0602/0019

Abstract

In this paper we establish some sufficient conditions for the oscillation of all solutions of the equation
$$
\Delta\left(r_n \Delta\left(x_n+p_n x_{n-k}\right)\right)+q_n \max _{[n-\ell, n]} x_s^\alpha=0, n \in N_0
$$
which improve and extend the known results. Examples are provided to illustrate the main results.

Keywords:

Second order, oscillation, neutral difference equation with “maxima”

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

S.Rajan Department of Mathematics, Erode Arts and Science College, Erode - 638 009, Tamil Nadu, India.
K.Malathi Department of Mathematics, Kongu Arts and Science College, Erode - 638 107, Tamil Nadu, India.

Pages: 417-419
Date Published: 01-04-2018
Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)

R.P. Agarwal, Difference Equations and Inequalities, Second Edition, Marcel Dekker, New York, 2000.

R.P.Agarwal, M.Bohner, S.R.Grace and D.O'Regan, Discrete Oscillation Theory, Hindawi Publ. Corp., New York, 2005.

R.Arul and M.Angayarkanni, Asymptotic behavior of second order nonlinear neutral difference equations with "maxima", Far East J. of Math. Sci, 82(1)2013, 79-92.

R.Arul and M.Angayarkanni, Oscillatory and asymptotic behavior of second order neutral difference equations with "maxima", JAM, (2014), 1916-1924.

I.Gyori and G.Ladas, Oscillation Theory of Delay Differential Equaitons with Applications, Claredan Press, Oxford, 1991.

G.H.Hardy, J.E.Littlewood and G.Polya, Inequalities,, Second Edition, Cambridge Uni. Press, Cambridge, 1998.

J.W.Luo and V.A.Petrov, Oscillation of second order neutral differece equaitons with "maxima", J. Math. Sci. Res. Hotline, 3(1999), 17-22.

J.W.Luo and D.D.Bainov, Oscillatory and asymptotic behavior of second order neutral differece equaitons with "maxima", J. Comput. Appl. Math., 131(2001), 333-341.

X.H.Tang and Y.J.Liu, Oscillation for nonlinear delay difference equations, Tamkang J.Math., 32(4)(2001), 275 280.

E.Thandapani and S.Selvarangam, Oscillation of second Emden-Fowler type neutral difference equations, Dyn. Cont. Dis. Impul. Sys., 19(2012), 453-469.