Asymptotic stability of solutions for a certain non-autonomous second-order stochastic delay differential equation

Authors: AHMED MOHAMED ABOU-EL-ELA, ABDEL-RAHIEM SADEK, AYMAN MOHAMMED MAHMOUD, EMAN SAYED FARGHALY

Abstract: In this paper, sufficient criteria that guarantee the existence of stochastic asymptotic stability of the zero solution of the nonautonomous second-order stochastic delay differential equation \eqref{3e1} were established with the aid of a suitable Lyapunov functional. Two examples are given in the last section to illustrate our main result.

Keywords: Asymptotic stability, nonautonomous second-order stochastic delay differential equation, Lyapunov functional

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