Table of Contents
International Journal of Analysis
Volume 2016, Article ID 2012315, 11 pages
Research Article

Stability and Boundedness of Solutions to a Certain Second-Order Nonautonomous Stochastic Differential Equation

1Research Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria
2Institute for Systems Science & Research and Postgraduate Support Directorate, Durban University of Technology, Durban 4000, South Africa

Received 28 July 2016; Revised 9 November 2016; Accepted 27 November 2016

Academic Editor: Ying Hu

Copyright © 2016 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.


This paper focuses on stability and boundedness of certain nonlinear nonautonomous second-order stochastic differential equations. Lyapunov’s second method is employed by constructing a suitable complete Lyapunov function and is used to obtain criteria, on the nonlinear functions, that guarantee stability and boundedness of solutions. Our results are new; in fact, according to our observations from the relevant literature, this is the first attempt on stability and boundedness of solutions of second-order nonlinear nonautonomous stochastic differential equations. Finally, examples together with their numerical simulations are given to authenticate and affirm the correctness of the obtained results.