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IJAMR International Journal of Applied Mathematical Research E-ISSN 2227-4324

Oscillation Criteria Of Third Order Nonlinear Neutral Differential equations

Authors and Affiliations

  • A.A. Soliman
  • R.A. Sallam
  • A. Elbitar
  • A.M. Hassan Faculty of science , Benha University ,Egypt

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Abstract

In this paper we will study the criteria for oscillation of the equation[a(t)(z"(t))]' +\sum_j=1^m fj(t; x(j(t))) = 0and establish new oscillation criteria some examples of the obtained results are given.Our technique is Riccati's method.Keywords: Oscillation, Third order, Nonlinear equation, Neutral type.

Author Biography

  • A.M. Hassan, Faculty of science , Benha University ,Egypt

    Demonstrator , Department of mathematics

References

[1] R. P. AGARWAL,SHIOW-LING SHIEH AND CHEH-CHIH YEH, Oscillation Criteria for Second-Order Retarded Differential Equations, Math. Comput. Modelling Vol. 26, No. 4, pp. l-11.

[2] B. Baculkov, E.M. Elabbasy, S.H. Saker, J. Dzurina, Oscillation criteria for third-order nonlinear differential equations, Math. Slovaca 58 (2) (2008) 1-20.

[3] B. Baculkov, J. Dzurina, Oscillation of third-order neutral differential equations, Mathematical and Computer Modelling 52 (2010) 215-226.

[4] S.H. Saker, Oscillation criteria of certain class of third-order nonlinear delay differential equations,Math. Slovaca 56 (2006) 433-450.

[5] J. Dzurina, I.P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140 (2003) 445-453.

View more references (11)

[6] Jiu-Gang Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Computers and Mathematics with Applications 59 (2010) 3710-3717.

[7] T. Kusano, Y. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Math. Hungar. 76 (1997) 81-99.

[8] ] G.S. Ladde, V. Lakshmikantham, B.G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York, 1987.

[9] L. Liu, Y. Bai, New oscillation criteria for second-order nonlinear neutral delay differential equations, J. Comput. Appl. Math. 231 (2009) 657-663.

[10] S.H. Saker, Oscillation criteria of certain class of third-order nonlinear delay differential equations, Math. Slovaca 56 (2006) 433-450.

[11] S. H. Saker; J. Dzurina, On the oscillation of certain class of third-order nonlinear delay differential equations, Mathematica Bohemica, Vol. 135 (2010), No. 3, 225-237.

[12] R.A.sallam, New Oscillation Criteria for Second Order Nonlinear Delay Differential Equations , International Journal of Nonlinear Science ,Vol.12(2011) No.1,pp.3-11.

Oscillation of third order nonlinear neutral differential equations 281

[13] Samir Saker , Oscillation Theory of Delay Differential and Difference Equations ’Second and Third Orders ’ VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG Dudweiler Landstr, Germany(2010) .

[14] R. Xu, F. Meng, Some new oscillation criteria for second order quasilinear neutral delay differential equations, Appl. Math. Comput. 182 (2006) 797-803.

[15] R. Xu, F. Meng, Oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput. 192 (2007) 216-222.


How to Cite

Soliman, A., Sallam, R., Elbitar, A., & Hassan, A. (2012). Oscillation Criteria Of Third Order Nonlinear Neutral Differential equations. International Journal of Applied Mathematical Research, 1(3), 268-281. https://doi.org/10.14419/ijamr.v1i3.95