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.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

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.

Bounded solutions of functional differential equations of the neutral type with infinite delays

1982 ◽  
Vol 93 (1-2) ◽  
pp. 33-39 ◽  
Author(s):  
V. G. Angelov ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Initial Value ◽  
Infinite Delays ◽  
Functional Differential

SynopsisIn this paper the authors obtain sufficient conditions for the existence and uniqueness of the initial value problem of functional differential equations of neutral type with infinite delays, making use of some earlier results of the present authors.

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