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New Results on Oscillation of even Order Neutral Differential Equations with Deviating Arguments

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DOI: 10.4236/apm.2011.13011    5,202 Downloads   10,437 Views   Citations

ABSTRACT

In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.

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L. Li and F. Meng, "New Results on Oscillation of even Order Neutral Differential Equations with Deviating Arguments," Advances in Pure Mathematics, Vol. 1 No. 3, 2011, pp. 49-53. doi: 10.4236/apm.2011.13011.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] R. P. Agarwal, S. R. Grace and D. ORegan, “Oscillation Theory for Differential Equations,” Kluwer Academic, Dordrecht, 2000.
[2] R. P. Agarwal and S. R. Grace, “The Oscillation of Higher Order Differential Equations with Deviating Arguments,” Computers & Mathematics with Applications, Vol. 38, No. 3-4, 1999, pp. 185-199. doi:10.1016/S0898-1221(99)00193-5
[3] Y. Bolat and O. Akin, “Oscillatory Behavior of Higher Order Neutral Type Nonlinear Forced Differential Equation with Oscillating Coefficients,” Journal of Mathematical Analysis and Applications, Vol. 290, No. 1, 2004, pp. 302-309. doi:10.1016/j.jmaa.2003.09.062
[4] W. N. Li, “Oscillation of Higher Order Delay Differential Equations of Neutral Type,” The Georgian Mathematical Journal, Vol. 7, No. 2, 2000, pp. 347-353.
[5] Ch. G. Philos, “Oscillation Theorems for Linear Differential Equations of Second Order,” Archiv der Mathematik, Vol. 53, No. 5, 1989, p. 483. doi:10.1007/BF01324723
[6] F. Meng and R. Xu, “Kamenev-Type Oscillation Criteria for Even Order Neutral Differential Equations with Deviating Arguments,” Applied Mathematics and Computation, Vol. 190, No. 2, 2007, pp. 1402-1408. doi:10.1016/j.amc.2007.02.017
[7] Yu. V. Rogovchenko and F. Tuncay, “Oscillation Criteria For Second-Order Nonlinear Differential Equations with Damping,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 69, No. 1, 2008, pp. 208-221. doi:10.1016/j.na.2007.05.012

  
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