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**A. M. A. Abou-El-Ela**

Department of Mathematics,

Faculty of Science,

Assiut University.

Assiut 71516, Egypt.

**A. I. Sadek**

Department of Mathematics,

Faculty of Science,

Assiut University.

Assiut 71516, Egypt.

**A. M. Mahmoud**

Department of Mathematics,

Faculty of Science,

New Valley Branch,

Assiut University.

New Valley, El-Khargah 72111, Egypt.

In this paper, by constructing Lyapunov functionals we investigate sufficient conditions, for the stochastic asymptotic stability of the zero solution of certain second-order stochastic differential equations with delay. By defining an appropriate Lyapunov functionals, we prove two new theorems on the stochastic asymptotic stability. Our results improve and form a complement to some known recent results in the literature.

- asymptotic stability
- delay
- Lyapunov functional
- stochastic differential equations

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