Some sufficient conditions for exponential stability of linear neutral functional differential equations

2005 ◽  
Vol 170 (1) ◽  
pp. 515-530
Author(s):  
Pham Huu Anh Ngoc ◽  
Byung Soo Lee
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

On stability of nonlinear neutral functional differential equations

2017 ◽  
Vol 24 (1) ◽  
pp. 89-104 ◽  
Author(s):  
Pham Huu Anh Ngoc ◽  
Thai Bao Tran ◽  
Cao Thanh Tinh
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Challenging Problem ◽  
Neutral Functional Differential Equations ◽  
Novel Approach ◽  
Functional Differential

We address the challenging problem of the exponential stability of nonlinear time-varying functional differential equations of neutral type. By a novel approach, we present explicit sufficient conditions for the exponential stability of nonlinear time-varying neutral functional differential equations. A discussion of the obtained results and illustrative examples are given.

Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems

1991 ◽  
Vol 43 (5) ◽  
pp. 1098-1120 ◽  
Author(s):  
Jianhong Wu ◽  
H. I. Freedman
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Stability And Convergence ◽  
Strong Monotonicity ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential ◽  
Monotone Dynamical Systems

AbstractThis paper is devoted to the machinery necessary to apply the general theory of monotone dynamical systems to neutral functional differential equations. We introduce an ordering structure for the phase space, investigate its compatibility with the usual uniform convergence topology, and develop several sufficient conditions of strong monotonicity of the solution semiflows to neutral equations. By applying some general results due to Hirsch and Matano for monotone dynamical systems to neutral equations, we establish several (generic) convergence results and an equivalence theorem of the order stability and convergence of precompact orbits. These results are applied to show that each orbit of a closed biological compartmental system is convergent to a single equilibrium.

scholarly journals Existence and Exponential Stability of Solutions to Stochastic Neutral Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ling Hu ◽  
Zheng Wu ◽  
Zhangzhi Wei ◽  
Lianglong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Banach Fixed Point Theorem ◽  
Stability Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Semigroup Approach ◽  
Existence And Stability ◽  
Functional Differential

In this paper we consider the existence and stability of solutions to stochastic neutral functional differential equations with finite delays. Under suitable conditions, the existence and exponential stability of solutions were obtained by using the semigroup approach and Banach fixed point theorem.

Existence of positive periodic solutions for a class of second-order neutral functional differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
He Yang ◽  
Lu Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fixed Point Index ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Index Theory ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Fixed Point Index Theory ◽  
Functional Differential

Abstract In this paper, under some ordered conditions, we investigate the existence of positive ω-periodic solutions for a class of second-order neutral functional differential equations with delayed derivative in nonlinearity of the form (x(t) − cx(t − δ))″ + a(t)g(x(t))x(t) = λb(t)f(t, x(t), x(t − τ 1(t)), x′(t − τ 2(t))). By utilizing the perturbation method of a positive operator and the fixed point index theory in cones, some sufficient conditions are established for the existence as well as the non-existence of positive ω-periodic solutions.

scholarly journals Asymptotically power solutions of higher order neutral functional differential equations

2004 ◽  
Vol 35 (4) ◽  
pp. 383-389
Author(s):  
Zhi-Qiang Zhu ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Neutral Functional Differential Equations ◽  
Polynomial Solutions ◽  
Functional Differential ◽  
Necessary And Sufficient

Necessary and sufficient conditions are derived for the existence of asymptotically polynomial solutions of a class of neutral functional differential equations.

scholarly journals EXISTENCE OF SOLUTIONS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

1999 ◽  
Vol 30 (4) ◽  
pp. 299-309
Author(s):  
K. BALACHANDRAN ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Cosine Families ◽  
Functional Differential

Sufficient conditions for existence of mild solutions for second order neutral functional differential equations are established by using the theory of strongly continuous cosine families and the Schaefer theorem.

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