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.


34K20 Stability theory of functional-differential equations