Almost Oscillation Criteria for Second Order Neutral Difference Equations

M. Angayarkanni; S. Kavitha

M. Angayarkanni Department of Mathematics, Kandaswami Kandar’s College, Velur 638 182, Namakkal (Dt), Tamil Nadu, India
S. Kavitha Department of Mathematics, Kandaswami Kandar’s College, Velur 638 182, Namakkal (Dt), Tamil Nadu, India

Keywords: Second order difference equation, Almost oscillatory, Riccati technique, Summation by parts.

Abstract

In this paper, we consider the second order neutral difference equation of the form ∆ (an(∆zn) α ) + qnx β n−σ = en, n ≥ n0, where zn = xn + pnxn−τ and α > 0, β > 0 are the ratios of odd positive integers. Examples are provided to illustrate the results.

Downloads

Download data is not yet available.

References

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.P. Agarwal, M.M.S. Manuel and E. Thandapani, Oscillatory and nonoscillatory behavior of second order delay difference equations, Appl. Math. Lett., 10(2)(1997), 103-109.

J. Cheng, Existence of nonoscillatory solution of second order linear difference equations, Appl. Math. Lett., 20(2007), 892-899.

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

R. Jankowski and E. Schmeidel, Almost oscillation criterca for second order neutral difference equations with quasi-differences, International Journal of Difference Equations, 9(1)(2014), 77-86.

J. Jiang, Oscillation criteria for second order quasilinear neutral delay difference equations, Appl. Math. Comput., 125(2002), 287-293.

W.G. Kelley and A.C. Peterson, Difference Equations: An Introduction with Applications, Acad. Press, New York, 1991.

G. Ladas, Ch.G. Philos and Y.G. Sticas, Sharp condition for the oscillation of delay difference equations, J. Appl. Math. Simul., 2(2)(1989), 101-112.

H.J. Li and C.C. Yeh, Oscillation criteria for second order neutral delay difference equations, Comput. Math. Appl., 36(1999), 123-132.

E. Thandapani, J.R. Graef and P.W. Spikes, On the oscillation of second order quasilinear difference equations, Nonlinear World, 3(1996), 545-565.

E. Thandapani and K. Mahalingam, Oscillation and nonoscillation of second order neutral difference equations, Czechoslovak Math. J., 53(128)(2003), 935-947.

E. Thandapani and S. Selvarangam, Oscillation theorems for second order nonlinear neutral difference equations, J. Math. Comput. Sci., 2(4)(2012), 866-879.

E. Thandapani, S. Selvarangam, R. Rama and M. Madhan, Improved oscillation criteria for second order nonlinear delay difference equations with nonpositive neutral term, Fasciculi Mathematici, 2016.

E. Thandapani, E. Vijaya and M. Gyori, New oscillation criteria for forced super-linear neutral type difference equations, Fasc. Math., (Pre-Print).