International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 12536, 13 pages
Convergence of Solutions of Certain Fourth-Order Nonlinear Differential Equations
1Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria
2Department of Pure and Applied Mathematics, University of Fort Hare, Alice 5700, South Africa
Received 4 September 2006; Revised 14 December 2006; Accepted 29 March 2007
Academic Editor: Thomas P. Witelski
Copyright © 2007 B. S. Ogundare and G. E. Okecha. 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.
We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature.