On stability and boundedness of solutions of a certain fourth-order delay differential equation
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 \textit{J. O. C. Ezeilo} in study of a related ordinary differential equation [J. Math. Anal. Appl. 5, 136- 146 (1962; Zbl 0107.296)].
fourth-order scalar delay-differential equation
scientific article; zbMATH DE number 4142519