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On asymptotic stability of solutions to third order nonlinear differential equations with retarded argument. (English) Zbl 1139.34054

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:

34K20 Stability theory of functional-differential equations
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