OSCILLATION OF THE EVEN-ORDER NONLINEAR
NEUTRAL DIFFERENTIAL EQUATIONS

Abstract

The oscillation criteria are investigated for all solutions of even-order neutral differential equations. The obtained results are based on the new comparison theorems, that enable us to reduce the problem of the oscillation of the higher order equation to the oscillation of the first order equation. The obtained comparison principles essentially simplify the examination of the studied equations.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 6
Year: 2018

DOI: 10.12732/ijam.v31i6.11

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References

  1. [1] J.K. Hale, Theory of Functional Differential Equations, Springer, New York, 2nd Ed., 1977.
  2. [2] R.D. Driver, A mixed neutral system, Nonlinear Analysis: Theory, Methods & Applications, 8, No 2 (1984), 155-158.
  3. [3] G.S. Ladde, V. Lakshmikanthan and B.G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, Inc., New York, 1987.
  4. [4] Ch.G. Philos, On the existence of nonoscillatory solutions tending to zero at∞for differential equations with positive delays, Archiv der Mathematik, 36 (1981), 168-178.
  5. [5] I.T. Kiguradze, T.A. Chanturiya, Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Kluwer Academic Publishers, Dordrecht, 1993. Tranl. from the 1985 Russian original.
  6. [6] A. Zafer, Oscillation criteria for even order neutral differential equations, Applied Mathematics Letters, 11 (1998), 21-25.
  7. [7] F.W. Meng, R. Xu, Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments, Applied Mathematics and Computation, 190 (2007), 458-464.
  8. [8] J. Dˇzurina and B. Bacul´ıkov´a, Oscillation of even-order neutral differential equations via comparison principles, Carpathian Journal of Mathematics, 30, No 3 (2014), 293-300.
  9. [9] J. Dˇzurina and B. Bacul´ıkov´a, Oscillation theorems for higher order neutral differential equations, Applied Mathematics and Computation, 219 (2012), 3769-3778.
  10. [10] J. Dˇzurina, B. Bacul´ıkov´a, T. Li, Oscillation results for even-order quasilinear neutral functional differential equations, Electronic Journal of Differential Equations, 143 (2011), 19.
  11. [11] T. Li, Z. Han, P. Zhao, S. Sun, Oscillation of even-order neutral delay differential equations, Advances in Difference Equations, 2010 (2010), 19.
  12. [12] M. Sathish Kumar, S. Janaki and V. Ganesan, Some new oscillatory behavior of certain third-order nonlinear neutral differential equations of mixed type, International Journal of Applied and Computational Mathematics (2018), 4, # 78.
  13. [13] V. Ganesan and M. Sathish Kumar, Oscillation of certain third order nonlinear differential equation with neutral terms, Bangmod International Journal of Mathematical & Computational Science, 3, No 1-2 (2017), 5360.
  14. [14] V. Ganesan, M. Sathish Kumar, S. Janaki and O. Moaaz, Nonlinear oscillation of certain third-order neutral differential equation with distributed delay, Journal of Mahani Mathematical Research Center, 7, No 1 (2018), 1-12.
  15. [15] V. Ganesan and M. Sathish Kumar, On the oscillation of a third order nonlinear differential equations with neutral type, Ural Mathematical Journal, 3, No 2 (2017), 122-129.
  16. [16] C. Zhang, R.P. Agarwal, M. Bohner, T. Li, New results for oscillatory behavior of even-order half-linear delay differential equations, Applied Mathematics Letters, 26 (2013), 179183.
  17. [17] Q. Zhang, J. Yan, Oscillation behavior of even order neutral differential equations with variable coefficients, Applied Mathematics Letters, 19 (2006), 12021206.