Uniform Asymptotic Stability of Abstract Functional Differential Equations

Asymptotic Stability of Solutions to Abstract Differential Equations

An evolution problem for abstract differential equations is studied. The typical problem is: u̇ = A(t)u+F(t,u), t ≥ 0; u(0) = u0; u̇ = du dt (∗) Here A(t) is a linear bounded operator in a Hilbert spaceH, and F is a nonlinear operator, ‖F(t,u)‖≤ c0‖u‖, p > 1, c0, p = const > 0. It is assumed that Re(A(t)u,u) ≤ −γ(t)‖u‖2 ∀u ∈ H, where γ(t) > 0, and the case when limt→∞ γ(t) = 0 is also considered....

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