Oscillatory Behavior of Second Order Neutral Dierence Equations with Mixed Neutral Term
DOI:
https://doi.org/10.24297/jam.v13i4.6231Keywords:
Oscillation, second order,, eutral dierence equation,, mixed neutral term.Abstract
In this paper, we study the oscillatory behavior of solution of second order neutral dierence equation with mixed neutral term of the form
(an(zn)) + qnx(n) = 0; n 2 N0; where zn = xn + bnxnô€€€l + cnxn+k and 1P
s=n0
1
as
= 1. We obtain some new oscilla-tion criteria for second order neutral dierence equation. Examples are presented to illustrate the main results.
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References
[1] R.P. Agarwal, Dierence Equations and Inequalities, Second Edition, Marcel Dekker, New York, 2000.
[2] R.P. Agarwal, M. Bohner, S.R. Grace and D.'O. Regan, Discrete Oscillation Theory, Hindawi Publ. Corp., New York, 2005.
[3] R.P. Agarwal, M.M.S. Manuel and E. Thandapani, Oscillatory and nonoscillatory be-havior of second order delay dierence equations, Appl. Math. Lett., 10(2)(1997), 103-109.
[4] J. Cheng, Existence of nonoscillatory solution of second order linear dierence equa- tions, Appl. Math. Lett., 20(2007), 892-899.
[5] I. Gyori and G. Ladas, Oscillation Theory of Delay Dierential Equations with Appli-cations, Clarendon Press, Oxford, 1991.
[6] J. Jiang, Oscillation criteria for second order quasilinear neutral delay dierence equa-tions, Appl. Math. Comput., 125(2002), 287-293.
[7] W.G. Kelley and A.C. Peterson, Dierence Equations: An Introduction with Applica-tions, Acad. Press, New York, 1991.
[8] G. Ladas, Ch.G. Philos and Y.G. Sticas, Sharp condition for the oscillation of delay dierence equations, J. Appl. Math. Simul., 2(2)(1989), 101-112.
[9] H.J. Li and C.C. Yeh, Oscillation criteria for second order neutral delay dierence equations, Comput. Math. Appl., 36(1999), 123-132.
[10] E. Thandapani, J.R. Graef and P.W. Spikes, On the oscillation of second order quasi-linear dierence equations, Nonlinear World, 3(1996), 545-565.
[11] E. Thandapani and K. Mahalingam, Oscillation and nonoscillation of second order neutral dierence equations, Czechoslovak Math. J., 53(128)(2003), 935-947.
[12] E. Thandapani and S. Selvarangam, Oscillation theorems for second order nonlinear neutral dierence equations, J. Math. Comput. Sci., 2(4)(2012), 866-879.
[2] R.P. Agarwal, M. Bohner, S.R. Grace and D.'O. Regan, Discrete Oscillation Theory, Hindawi Publ. Corp., New York, 2005.
[3] R.P. Agarwal, M.M.S. Manuel and E. Thandapani, Oscillatory and nonoscillatory be-havior of second order delay dierence equations, Appl. Math. Lett., 10(2)(1997), 103-109.
[4] J. Cheng, Existence of nonoscillatory solution of second order linear dierence equa- tions, Appl. Math. Lett., 20(2007), 892-899.
[5] I. Gyori and G. Ladas, Oscillation Theory of Delay Dierential Equations with Appli-cations, Clarendon Press, Oxford, 1991.
[6] J. Jiang, Oscillation criteria for second order quasilinear neutral delay dierence equa-tions, Appl. Math. Comput., 125(2002), 287-293.
[7] W.G. Kelley and A.C. Peterson, Dierence Equations: An Introduction with Applica-tions, Acad. Press, New York, 1991.
[8] G. Ladas, Ch.G. Philos and Y.G. Sticas, Sharp condition for the oscillation of delay dierence equations, J. Appl. Math. Simul., 2(2)(1989), 101-112.
[9] H.J. Li and C.C. Yeh, Oscillation criteria for second order neutral delay dierence equations, Comput. Math. Appl., 36(1999), 123-132.
[10] E. Thandapani, J.R. Graef and P.W. Spikes, On the oscillation of second order quasi-linear dierence equations, Nonlinear World, 3(1996), 545-565.
[11] E. Thandapani and K. Mahalingam, Oscillation and nonoscillation of second order neutral dierence equations, Czechoslovak Math. J., 53(128)(2003), 935-947.
[12] E. Thandapani and S. Selvarangam, Oscillation theorems for second order nonlinear neutral dierence equations, J. Math. Comput. Sci., 2(4)(2012), 866-879.
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Published
2016-08-03
How to Cite
Angayarkanni, M., & Kavitha, S. (2016). Oscillatory Behavior of Second Order Neutral Dierence Equations with Mixed Neutral Term. JOURNAL OF ADVANCES IN MATHEMATICS, 13(4), 7302–7307. https://doi.org/10.24297/jam.v13i4.6231
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