On stability and boundedness of solutions of a certain fourth-order delay differential equation. (English) Zbl 0697.34063

Okoronkwo, Emmanuel O.

Int. J. Math. Math. Sci. 12, No. 3, 589-602 (1989).

A Razumikhin-type theorem is used to obtain sufficient conditions for uniform asymptotic stability and boundedness of solutions of a fourth- order scalar delay-differential equation of the form \[ x^{''''}(t)+f(x''(t))x'''(t)+\alpha_ 2x''(t)+\beta_ 2x''(t- h)+g(x'(t-h))+\alpha_ 4x(t)+\beta_ 4x(t-h)=P(t). \] The proof utilizes a Lyapunov function obtained by J. O. C. Ezeilo in study of a related ordinary differential equation [J. Math. Anal. Appl. 5, 136- 146 (1962; Zbl 0107.296)].

Reviewer: L.I.Grimm

MSC:

34K99	Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K20	Stability theory of functional-differential equations
34D20	Stability of solutions to ordinary differential equations
34C11	Growth and boundedness of solutions to ordinary differential equations

Keywords:

Razumikhin-type theorem; uniform asymptotic stability; boundedness of solutions; fourth-order scalar delay-differential equation; Lyapunov function

Citations:

Zbl 0107.296