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Zbl 1215.34079
Tunç, Cemil
Stability and bounded of solutions to non-autonomous delay differential equations of third order.
(English)
[J] Nonlinear Dyn. 62, No. 4, 945-953 (2010). ISSN 0924-090X; ISSN 1573-269X/e

Summary: 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 $$\dddot{x}(t)+a(t)\varphi(\dot{x}(t))\ddot{x}(t)+b(t)\psi(\dot{x}(t))+c(t)h(x(t-r))=p(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t)),$$ 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 Lyapunov functional approach, we prove two new results on the subject.
MSC 2000:
*34K12 Properties of solutions of functional-differential equations
34K20 Stability theory of functional-differential equations

Keywords: boundedness; stability; non-autonomous; differential equation; third order; delay

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