Opuscula Math. 37, no. 6 (2017), 839-852

Opuscula Mathematica

Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation

John R. Graef
Ercan Tunҫ
Said R. Grace

Abstract. This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.

Keywords: third order, neutral differential equations, asymptotic behavior, nonoscillatory, oscillatory solution.

Mathematics Subject Classification: 34K10, 34K11, 34K15, 34C10.

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  • John R. Graef
  • University of Tennessee at Chattanooga, Department of Mathematics, Chattanooga, TN 37403, USA
  • Ercan Tunҫ
  • Gaziosmanpasa University, Department of Mathematics, Faculty of Arts and Sciences, 60240, Tokat, Turkey
  • Said R. Grace
  • Department of Engineering Mathematics, Faculty of Engineering, Cairo University Orman, Giza 12221, Egypt
  • Communicated by Alexander Domoshnitsky.
  • Received: 2016-09-01.
  • Revised: 2017-01-01.
  • Accepted: 2017-02-07.
  • Published online: 2017-09-28.
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Cite this article as:
John R. Graef, Ercan Tunҫ, Said R. Grace, Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation, Opuscula Math. 37, no. 6 (2017), 839-852, http://dx.doi.org/10.7494/OpMath.2017.37.6.839

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