Differential Equations Of Neutral Type Research Articles

Absolutely continuous global solutions of the initial value problem for neutral functional differential equations of mixed type

The paper considers initial value problems for functional differential equations of neutral type with deviations dependent on the required function and its derivative. By the help of the method of accretive operators natural sufficient conditions have been obtained which guarantee the existence and uniqueness of the absolutely continuous global solution of the problem set to be solved.

The Numerical Solution of Volterra Functional Differential Equations of Neutral Type

In this paper methods of Adams–Moulton type for neutral functional differential equations are investigated. A general convergence theorem is presented and the order of convergence of these methods is examined. Some numerical examples are given.

One step methods for the numerical solution of volterra functional differential equations of neutral type

A class of numerical methods for neutral functional differential equations is considered. The convergence theorem is given. The somewhat pessimistic result is shown that Tavernini's scheme for constructing methods of arbitrary order fails in the case of neutral functional differential equations

A Neutral Functional Differential Equation of Lurie Type

The problem of Lurie is posed for systems described by a functional differential equation of neutral type. Sufficient conditions are obtained for absolute stability for the controlled system if it is assumed that the uncontrolled plant equation is uniformly asymptotically stable. Both the direct and indirect control cases are treated.

Eine Existenzaussage f�r asymptotisch lineare St�rungen eines Fredholmoperators mit Index O

Let X, Y be Banach spaces, L: X ⊃ Dom(L)→Y a linear Fredholm operator with Fredholm index zero, and T a asymptotic linear k-set contraction with k∈[0, 1(L)), where 1(L) denotes the lower bound of L with respect to the set-measure of noncampactness. Using coincidence degree we deduce a Fredholm alternative for the equation Lx=Tx+y (y∈Y), which involves the results of [11] and [17] in the case X=Y and L=Id. Applications are given for a functional differential equation of neutral type and for a boundary value problem of a second order differential equation.

Representation of the solutions of quasilinear functional differential equations of neutral type in case of resonance

Representation of the solutions of quasilinear functional differential equations of neutral type in case of resonance

Criteria for Function Space Controllability of Linear Neutral Systems

Necessary and sufficient conditions for the exact state controllability of the linear autonomous differential difference equation of neutral type, $\dot x(t) = A_{ - 1} \dot x(t - h) + A_0 x(t) + A_1 x(t - h) + Bu(t)$, are given for the Sobolev state space $W_2^{(1)} ([ - h,0],R^n )$. In particular when B is an $n \times 1$ matrix, it is shown that the controllability of the above n-dimensional system on the interval $[0,\tau ]$, $\tau > nh$, is equivalent to rank $[B,A_{ - 1} B, \cdots ,A_{ - 1}^{n - 1} B] = n$ and that a certain two point boundary value problem for a related homogeneous ordinary differential equation have only the trivial solution. Practical criteria based thereon entail only elementary computations involving the coefficient matrices $[A_{ - 1} ,A_0 ,A_1 ,B]$ but these computations can be tedious when $n > 3$. The condition that the two point boundary value problem have only the trivial solution is often equivalent to a much simpler condition: $K(\lambda )\mathcal{S}_\lambda ^n \ne 0$ f...

Asymptotically autonomous neutral functional differential equations with time-dependent lag

Publisher Summary This chapter describes asymptotically autonomous neutral functional differential equations with time-dependent lag. The aim is to extend, for a system of functional differential equations of neutral type, the results obtained by Hale and Cooke for retarded equations and by Ize for neutral equations with constant lag. Haie considered a more general class of equations and was able to extend the results of Bellman and Cooke by proving that ∫∞ γ (t) dt

Linear functional differential equations of neutral type asymptotically autonomous

Linear functional differential equations of neutral type asymptotically autonomous

On the averaging principle for functional ? Differential equations of neutral type

On the averaging principle for functional ? Differential equations of neutral type

Linear functional differential equations of neutral type asymptotically autonomous

It is studied the relationship between the solutions of the linear functional differential equations(1) (d/dx) D(xt)=L(xt) and its perturbed equation(2) [(d/dx) D(xt)−G(t, xt)]= =L(xt)+F(t, xt) and is proved, under certain hypotheses which will be precised bellow that, if μ is a simple characteristic root of(1), then there exist a σ > 0 and a non zero vector a such that system(2) has a solution satisfying $$\alpha (t) = exp\left( {\mu (t - \sigma ) + \int\limits_\sigma ^t {\delta (s)ds} } \right) [a + o(1)],$$ where δ(t)=αd{F(t, ϕμ)+μG(t, ϕμ)+F(t, X0G(t, ϕμ))}, ϕμ(θ)=c·exp (μθ), −r⩾θ⩾0 and α, d, X0 are given constants.

A First Order Method for Differential Equations of Neutral Type

A first order method is presented for solution of the initial-value problem for a differential equation of neutral type with implicit delay in the critical case where the time-lag is zero and the method of stepwise integration does not apply. A convergence theorem is proved, and numerical examples are given.

A first order method for differential equations of neutral type

A first order method is presented for solution of the initial-value problem for a differential equation of neutral type with implicit delay in the critical case where the time-lag is zero and the method of stepwise integration does not apply. A convergence theorem is proved, and numerical examples are given.

An investigation of the stability in a critical case of certain null roots of a system of differential equations of neutral type

An investigation of the stability in a critical case of certain null roots of a system of differential equations of neutral type

Existence and uniqueness theorems for some functional differential equations of neutral type

Existence and uniqueness theorems for some functional differential equations of neutral type

Analytic solutions of a neutral differential equation near a singular point

Fixed point techniques are employed to prove existence and uniqueness of a holomorphic solution to a functional differential equation of neutral type in the neighborhood of a regular singular point.

The stability of systems of differential equations of neutral type

The stability of systems of differential equations of neutral type

Stability of functional differential equations of neutral type

Abstract : A functional differential equation of neutral type is a differential system in which the rate of change of the system depends not only upon the past history but also the derivative of the past history of the system. For example, the system (1.1) x dot (t) + A x dot (t - 1) = f(t,x(t),x(t - 1)) is a functional differential or differential difference equation of neutral type. It is the purpose of this paper to give sufficient conditions for the stability and instability of solutions of a large class of equations (1.1) in terms of functions similar to those occurring in the application of the second method of Liapunov to ordinary and functional differential equations of retarded type. The basic restriction on the class of systems is that the derivatives occur linearly with coefficients depending only upon t and that the 'difference' operator associated with the equation is stable. (Author)

Periodic solutions of systems of n-th order differential equations of neutral type with retarded argument

Periodic solutions of systems of n-th order differential equations of neutral type with retarded argument