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

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  • A. T. Ademola
  • S. Moyo
  • B. S. Ogundare
  • M. O. Ogundiran
  • O. A. Adesina

Abstract

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.

Suggested Citation

  • A. T. Ademola & S. Moyo & B. S. Ogundare & M. O. Ogundiran & O. A. Adesina, 2016. "Stability and Boundedness of Solutions to a Certain Second-Order Nonautonomous Stochastic Differential Equation," International Journal of Analysis, Hindawi, vol. 2016, pages 1-11, December.
    • Handle: RePEc:hin:ijanal:2012315
    DOI: 10.1155/2016/2012315
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    References listed on IDEAS

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    1. Wenli Zhu & Jiexiang Huang & Xinfeng Ruan & Zhao Zhao, 2014. "Exponential Stability of Stochastic Differential Equation with Mixed Delay," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, March.
    2. A. T. Ademola & B. S. Ogundare & M. O. Ogundiran & O. A. Adesina, 2016. "Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-10, August.
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    Cited by:

    1. M. De la Sen, 2018. "On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching," Journal of Mathematics, Hindawi, vol. 2018, pages 1-16, January.

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