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Nonlinear Dynamics

, Volume 62, Issue 4, pp 945–953 | Cite as

Stability and bounded of solutions to non-autonomous delay differential equations of third order

  • Cemil Tunç
Original Paper

Abstract

In this paper, we obtain some sufficient conditions to guarantee the uniform asymptotic stability of zero solution and bounded of all solutions to non-autonomous delay differential equation of third order
$$\begin{array}{@{}ll}\vspace*{-1pt}&\dddot{x}(t)+a(t)\varphi\bigl(\dot{x}(t)\bigr)\ddot{x}(t)+b(t)\psi\bigl(\dot{x}(t)\bigr)\\[5pt]&\qquad{}+c(t)h\bigl(x(t-r)\bigr)\\[5pt]&\quad =p\bigl(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t)\bigr),\vspace*{-1pt}\end{array}$$
when \(p(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t))=0\) and \(p(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t))\ne 0\), respectively. By using the Liapunov functional approach, we prove two new results on the subject.

Keywords

Boundedness Stability Non-autonomous Differential equation Third order Delay 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and SciencesYüzüncü Yıl UniversityVanTurkey

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