New Oscillation Criteria for Second Order Neutral Type Dierence Equations
DOI:
https://doi.org/10.24297/jam.v13i4.6290Keywords:
Almost oscillation, second order,, neutral dierence equation.Abstract
In this paper, we present some new oscillation criteria for second order neutral type dierence equation of the form (an(zn)) + qnf(xn) = en; n n0 > 0; where zn = xn ô€€€pnxnô€€€l and is ratio of odd positive integers. Examples are provided to illustrate the 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-
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[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] R. Jankowski and E. Schmeidel, Almost oscillation criterca for second order neutral
dierence equations with quasi-dierences, International Journal of Dierence Equa-
tions, 9(1)(2014), 77-86.
[7] J. Jiang, Oscillation criteria for second order quasilinear neutral delay dierence equa-
tions, Appl. Math. Comput., 125(2002), 287-293.
[8] W.G. Kelley and A.C. Peterson, Dierence Equations: An Introduction with Applica-
tions, Acad. Press, New York, 1991.
[9] 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.
[10] H.J. Li and C.C. Yeh, Oscillation criteria for second order neutral delay dierence
equations, Comput. Math. Appl., 36(1999), 123-132.
[11] 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.
[12] E. Thandapani and K. Mahalingam, Oscillation and nonoscillation of second order
neutral dierence equations, Czechoslovak Math. J., 53(128)(2003), 935-947.
[13] E. Thandapani and S. Selvarangam, Oscillation theorems for second order nonlinear
neutral dierence equations, J. Math. Comput. Sci., 2(4)(2012), 866-879.
[14] E. Thandapani, S. Selvarangam, R. Rama and M. Madhan, Improved oscillation crite-
ria for second order nonlinear delay dierence equations with nonpositive neutral term,
Fasciculi Mathematici, 2016.
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] R. Jankowski and E. Schmeidel, Almost oscillation criterca for second order neutral
dierence equations with quasi-dierences, International Journal of Dierence Equa-
tions, 9(1)(2014), 77-86.
[7] J. Jiang, Oscillation criteria for second order quasilinear neutral delay dierence equa-
tions, Appl. Math. Comput., 125(2002), 287-293.
[8] W.G. Kelley and A.C. Peterson, Dierence Equations: An Introduction with Applica-
tions, Acad. Press, New York, 1991.
[9] 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.
[10] H.J. Li and C.C. Yeh, Oscillation criteria for second order neutral delay dierence
equations, Comput. Math. Appl., 36(1999), 123-132.
[11] 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.
[12] E. Thandapani and K. Mahalingam, Oscillation and nonoscillation of second order
neutral dierence equations, Czechoslovak Math. J., 53(128)(2003), 935-947.
[13] E. Thandapani and S. Selvarangam, Oscillation theorems for second order nonlinear
neutral dierence equations, J. Math. Comput. Sci., 2(4)(2012), 866-879.
[14] E. Thandapani, S. Selvarangam, R. Rama and M. Madhan, Improved oscillation crite-
ria for second order nonlinear delay dierence equations with nonpositive neutral term,
Fasciculi Mathematici, 2016.
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Published
2017-10-09
How to Cite
Angayarkanni, M. (2017). New Oscillation Criteria for Second Order Neutral Type Dierence Equations. JOURNAL OF ADVANCES IN MATHEMATICS, 13(4), 7346–7353. https://doi.org/10.24297/jam.v13i4.6290
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