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

International Journal of Analysis

S. Moyo¹  B. S. Ogundare²  A. T. Ademola²  M. O. Ogundiran²  O. A. Adesina² 

[1]Institute for Systems Science & Research and Postgraduate Support Directorate, Durban University of Technology, Durban 4000, South Africa, dut.ac.za

[2]Research Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria, oauife.edu.ng

DOI  :  10.1155/2016/2012315

学科分类：数学（综合）

来源: Hindawi Publishing Corporation

【 摘 要 】

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.

【 授权许可】

CC BY