International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 589-602
doi:10.1155/S0161171289000724
On stability and boundedness of solutions of a certain
fourth-order delay differential equation
Department of Mathematical Sciences, Loyola University, New Orleans 70118, Louisiana, USA
Received 12 February 1987; Revised 2 February 1988
Copyright © 1989 Emmanuel O. Okoronkwo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Using a Razumikhin - type theorem, we deduce sufficient conditions that
guarantee the uniform asymptotic stability and boundedness of solutions of a scalar
real fourth-order delay differential equation. The Lyapunov function constructed for
an ordinary fourth-order differential equation is seen to work for the delay system.