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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 3, Pages 589-602

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 Hindawi Publishing Corporation. 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.


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.