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Oscillation Criteria of Certain Third‐Order Differential Equation with Piecewise Constant Argument

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  • Haihua Liang
  • Gen-qiang Wang

Abstract

We study the oscillation and asymptotic behavior of third‐order nonlinear delay differential equation with piecewise constant argument of the form (r2(t)(r1(t)x′(t))′)′ + p(t)x′(t) + f(t, x([t])) = 0. We establish several sufficient conditions which insure that any solution of this equation oscillates or converges to zero. Some examples are given to illustrate the importance of our results.

Suggested Citation

  • Haihua Liang & Gen-qiang Wang, 2012. "Oscillation Criteria of Certain Third‐Order Differential Equation with Piecewise Constant Argument," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:498073
    DOI: 10.1155/2012/498073
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    References listed on IDEAS

    as
    1. S. M. Shah & Joseph Wiener, 1983. "Advanced differential equations with piecewise constant argument deviations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-33, January.
    2. H. A. Agwo, 1998. "Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 21, pages 1-5, January.
    3. Ravi P. Agarwal & Said R. Grace & Donal O’Regan, 2000. "Oscillation Theory for Difference and Functional Differential Equations," Springer Books, Springer, number 978-94-015-9401-1, October.
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    Cited by:

    1. Qi Wang & Jiechang Wen & Shenshan Qiu, 2013. "Euler‐Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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