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Erschienen in:
2013 | OriginalPaper | Buchkapitel
3. Stability of Linear Scalar Equations
verfasst von : Leonid Shaikhet
Erschienen in: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Verlag: Springer International Publishing
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Abstract
In Chap. 3 the procedure of constructing Lyapunov functionals is used to obtain conditions for the stability of scalar stochastic linear delay differential equations with constant and variable coefficients and with constant and variable delays. It is shown that different ways of constructing Lyapunov functionals for a given equation allow one to get different conditions for the asymptotic mean-square stability of the zero solution of this equation. In particular, linear differential equations with two delays and with n delays (n>2) in deterministic part and linear nth-order (n>1) differential equations are considered. The obtained results are illustrated by 23 figures with stability regions and stable or unstable solutions of considered equations.