Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term

• Autorzy: Thandapani, E. , Selvarangam, S. , Rama, R. , Madhan, M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form ∆(a_n (∆z_n )^α )+q_n f(x_n-σ) )=0, n>n_o >0, where z_n - x_n - p_n x_n-r, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.

Słowa kluczowe

EN

oscillation; second order delay difference equation; non-positive neutral term

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2016
• Tom: Nr 56
• Strony: 155--165
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Thandapani, E.

• Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai - 600 005, India ,

autor

Selvarangam, S.

• Department of Mathematics, Presidency College, Chennai - 600 005, India,

autor

Rama, R.

• Department of Mathematics, Quaid-e-Millath Government College for Women, Chennai - 600 002, India ,

autor

Madhan, M.

• Department of Mathematics, Presidency College, Chennai - 600 005, India ,

Bibliografia

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• [2] Agarwal R.P., Bohner M., Grace S.R., O'Regan D., Discrete Oscillation Theory, Hindawi Publ. Corp., New York, 2005.
• [3] Agarwal R.P., Grace S.R., Thandapani E., Oscillatory and nonoscillatory behavior of second order neutral delay difference equations, Math. Comp. Modelling, 24(1996), 5-11.
• [4] Gyori I., Ladas G., Oscillation Theory of Delay Differential Equations, Clarendon press, Oxford, 1991.
• [5] Saker S.H., Oscillation Theory of Delay Differential and Difference Equations: Second and Third Order, Verlag dr Muler, Germany, 2010.
• [6] Saker S.H., O'Regan D., New oscillation criteria for second order neutral functional dynamic equations via the generalized Riccati substitution, Commu. Nonlin. Sci. Numer. Simu., 16(2011), 423-434.
• [7] Saker S.H., O'Regan D., New oscillation criteria for second order neutral functional dynamic equations on time scales via Riccati substitution, Hiroshima Math. J., 42(2012), 77-98.
• [8] Sun Y.G., Saker S.H., Oscillation for second order nonlinear neutral delay difference equations, Appl. Math. Comput., 163(2005), 909-918.
• [9] Tang X.H., Liu Y., Oscillation for nonlinear delay difference equations, Tamkang J. Math., 32(2001), 275-280.
• [10] Thandapani E., Sundaram P., Graef J.R., Spikes P.W., Asymptotic properties of solutions of nonlinear second order neutral delay difference equations, Dynamic Sys. Appl., 4(1995), 125-136.
• [11] Thandapani E., Balasubramanian V., Graef J.R., Oscillation criteria for second order neutral difference equations with negative neutral term, Inter. J. Pure. Appl. Math., 87(2013), 283-292.
• [12] Thandapani E., Liu Z., Arul R., Raja P.S., Oscillation and asymptotic behavior of second order difference equations with nonlinear neutral terms, Appl.Math. E-Notes, 4(2004), 59-67.
• [13] Thandapani E., Mahalingam K., Necessary and sufficient conditions for oscillation of second order neutral delay difference equations, Tamkang J. Math., 34(2) (2003), 137-145.
• [14] Wang D.M., Xu Z.T., Oscillation of second order quasi-linear neutral delay difference equations, Acta Math. Appl. Sinica., 27(2011), 93-104.
• [15] Zafer A., Dahiya R.S., Oscillation of a neutral difference equations, Appl. Math. Lett., 6(1993), 71-74.
• [16] Zhou Z., Yu J., G. Lei, Oscillation for even order neutral difference equations, Korean J. Comput. Appl. Math., 7(2000), 601-610.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

Identyfikatory

DOI

10.1515/fascmath-2016-0011