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Zbl 1166.34329
Tunç, Cemil
Stability criteria for certain third order nonlinear delay differential equations.
(English)
[J] Port. Math. (N.S.) 66, No. 1, 71-80 (2009). ISSN 0032-5155; ISSN 1662-2758/e

Summary: We study the asymptotic stability of the trivial solution of third order nonlinear delay differential equation $$x'''(t) + f(x(t), x^\prime (t))x^{\prime \prime }(t) + g(x(t - r), x^\prime (t - r)) + h(x(t - r)) = 0,$$ where $r > 0$ is a constant delay. In proving our result we make use of Lyapunov's second method by constructing a Lyapunov functional.
MSC 2000:
*34K20 Stability theory of functional-differential equations

Keywords: asymptotic stability; Lyapunov functional; nonlinear delay differential equation of third order

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