On the uniform asymptotic stability in functional-differential equations

On the Uniform Asymptotic Stability of Functional Differential Equations of the Neutral Type

Abstract. Consider the functional equations of neutral type (1) (d/dt)D(t, x,) -/(*, *,) and (2) (d/dt) [D(t, x,) -G(t, *,)} =/(/, *,) + F(t, Xt) where D,f are bounded linear operators from C[a, b] into R" or C" for each fixed t in [0, °° ), F= Fi+Fh G = Gi+Gh | F¡(t, <*>) \ ¿v(t)\\, \Gx(t,4>)\ ¿Tr(t)\ 0, there exists 8(e) >0 such that | F2(t, 0)| á«|*|, |Gs...

Asymptotic stability of neutral stochastic functional integro-differential equations*

This paper is concerned with the existence and asymptotic stability in the p-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given in [8], and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achie...

Asymptotic Stability of Stochastic Impulsive Neutral Partial Functional Differential Equations

In this paper the authors study the existence and asymptotic stability in p-th moment of mild solutions to stochastic neutral partial differential equation with impulses. Their method for investigating the stability of solutions is based on the fixed point theorem.

Asymptotic stability for a class of functional differential equations

On the practical global uniform asymptotic stability of stochastic differential equations

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and th...