ON THE STABILITY AND BOUNDEDNESS OF SOLUTIONS TO CERTAIN SECOND ORDER NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

A. T. ADEMOLA, S. O. AKINDEINDE, B. S. OGUNDARE, M. O. OGUNDIRAN, O. A. ADESINA

Abstract


This paper emphases on stability and boundedness of solutions to certain nonlinear non autonomous second order stochastic delay differential equations. A complete Lyapunov functional is constructed and used to establish conditions, on the nonlinear functions appearing in the equations, to guarantee stability and boundedness of solutions to the second order stochastic delay differential equations considered. The obtained results are new, complement and extend the existing results on second order stochastic delay differential equations in the literature. Finally, examples together with their numerical simulations are given to confirm genuineness and assert the correctness of the obtained results.

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References


A.M.A. Abou-El-Ela, A.I. Sadek and A.M. Mahmoud, On the stability of solutions for certain second-order stochastic delay differential equations, Differential Equations and Control Processes, 2015, N 2, 2015.

A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud and R.O.A. Taie, On the stochastic stability and boundedness of solutions for stochastic delay differential equation of the second order, Chinese Journal of Mathematics, 2015, Article ID 358936, 8 pages, 2015.

A.T. Ademola, Boundedness and stability of solutions to certain second order differential equations, Differential Equations and Control Processes, 2015, N 3, 38 - 50, 2015.

A.T. Ademola, S. Moyo, B.S. Ogundare, M.O. Ogundiran and O.A. Adesina, Stability and boundedness of solutions to a certain second order non autonomous stochastic differential equation, International Journal of Analysis, 2016, Article ID 2012315, 11 pages, 2016.

A.T. Ademola, B.S. Ogundare, M.O. Ogundiran and O.A. Adesina, Periodicity, stability, and boundedness of solutions to certain second order delay differential equations, International Journal of Differential Equations, 2016, Article ID 2843709, 10 pages, 2016.


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