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International Journal of Differential Equations
Volume 2015, Article ID 213935, 12 pages
Research Article

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

Research Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria

Received 13 July 2015; Accepted 31 August 2015

Academic Editor: Nikolai N. Leonenko

Copyright © 2015 A. T. Ademola et al. 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.


The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples.