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Zbl 1139.34054
Tunç, Cemil
On asymptotic stability of solutions to third order nonlinear differential equations with retarded argument. (English)
[J] Commun. Appl. Anal. 11, No. 3-4, 515-528 (2007). ISSN 1083-2564

Summary: We are concerned with the asymptotic stability of the trivial solution of third order nonlinear delay different equations of the form $$x'''(t) + \varphi(x(t), x'(t))x''(t) +\psi(x(t - r(t)), x'(t -r(t))+ h(x(t-r(t))) = 0.$$ By constructing a Lyapunov functional, we establish some new sufficient conditions which insure that the trivial solution of this equation is asymptotically stable. An example is given to illustrate the result.

MSC 2000:: *34K20 Stability theory of functional-differential equations

Keywords: Lyapunov functional

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Zentralblatt MATH Berlin [Germany]