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

DOI

10.3906/mat-1508-62

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

First Page

576

Last Page

584

Recommended Citation

ABOU-EL-ELA, AHMED MOHAMED; SADEK, ABDEL-RAHIEM; MAHMOUD, AYMAN MOHAMMED; and FARGHALY, EMAN SAYED (2017) "Asymptotic stability of solutions for a certain non-autonomous second-order stochastic delay differential equation," Turkish Journal of Mathematics: Vol. 41: No. 3, Article 10. https://doi.org/10.3906/mat-1508-62
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/10