Neutral Functional Differential Equations Research Articles

Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps

In this paper, we are concerned with neutral stochastic functional differential equations driven by pure jumps (NSFDEwPJs). We prove the existence and uniqueness of the solution to NSFDEwPJs whose coefficients satisfying the local Lipschitz condition. In addition, we establish the p-th exponential estimations and almost surely asymptotic estimations of the solution for NSFDEwJs.

Existence Results for Fractional Neutral Functional Differential Equations with Random Impulses

In this paper, we investigate the existence of solutions for the fractional neutral differential equations with random impulses. The results are obtained by using Krasnoselskii’s fixed point theorem. Examples are added to show applications of the main results.

Non-densely defined impulsive neutral stochastic functional differential equations driven by fBm in Hilbert space with infinite delay

We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H ∈ (1/2, 1) in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.

Existence and continuous dependence of mild solutions for fractional neutral abstract evolution equations

This paper is mainly concerned with the existence, uniqueness and continuous dependence of mild solutions for fractional neutral functional differential equation with nonlocal initial conditions and infinite delay. The results are obtained by means of the classical fixed point theorems combined with theory of resolvent operators for integral equations.

The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results

We consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method. We give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments.

Forced Oscillation of Solutions of a Fractional Neutral Partial Functional Differential Equation

In this paper, we will establish the sufficient conditions for the oscillation of solutions of neutral time fractional partial differential equation of the form for where Ω is a bounded domain in RN with a piecewise smooth boundary is a constant, is the Riemann-Liouville fractional derivative of order a of u with respect to t and is the Laplacian operator in the Euclidean N-space RN subject to the condition

An Existence Result for Impulsive Stochastic Functional Differential Equations with Multiple Delays

In this paper we consider Impulsive stochastic neutral functional differential equations with multiple delays. By using Schaefer’s fixed point theorem, we prove the existence of solutions for stochastic differential equations with impulses

Boundedness and Oscillation of Third Order Neutral Differential Equations with Deviating Arguments

we consider the third-order neutral functional differential equations with deviating arguments. A new theorem is presented that improves a number of results reported in the literature. Examples are included to illustrate new results.

The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part II: Differential Equations with Deviating Arguments

We consider the numerical solution of boundary value problems for neutral differential equations with deviating arguments by the collocation method, which includes the finite element method and the spectral element method. By using the results of Part I [SIAM J. Numer. Anal., 53 (2015), pp. 2771--2793] of this paper, we obtain concrete convergence theorems for this particular type of functional differential equations.

Asymptotic behavior of solutions to neutral functional differential equations with infinite delay

Asymptotic behavior of solutions to neutral functional differential equations with infinite delay

Symmetric Hopf bifurcation in implicit neutral functional differential equations: Equivariant degree approach

In this paper, we develop a general framework for studying symmetric Hopf bifurcation phenomenon for (symmetric) implicit neutral functional differential equations (in short, INFDEs) satisfying appropriate compactness and nonexpansiveness conditions. The main abstract result, obtained by means of the twisted equivariant degree theory, establishes sufficient conditions for the occurrence of the Hopf bifurcation and provides a complete description of symmetric properties of bifurcating branches. The abstract result is supported by a concrete example of an INFDE admitting countably many Hopf bifurcation points and respecting D24-symmetries.

Almost Periodic Solutions of Neutral Delay Functional Differential Equations on Time Scales

In this paper, based on the properties of almost periodic function and exponential dichotomy of linear system on time scales as well as Krasnoselskii’s fixed point theorem, some sufficient conditions are established for the existence of almost periodic solutions of delayed neutral functional differential equations on time scales. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.

Retarded Neutral Stochastic Equations Driven by Multiplicative Fractional Brownian Motion

In this article, we develop an existence and uniqueness theory of pathwise mild solutions for a class of stochastic neutral partial functional differential equations that are driven by an infinite-dimensional multiplicative fractional noise. Our existence and uniqueness result is divided into two parts: first we establish the existence and uniqueness of a local solution, which proof rests upon the Banach fixed point theorem; then the existence of a unique global solution is based on certain regularity properties of the local solution as well as a suitable way of extending the local solution to the entire interval in finitely many steps.

Periodic solutions for a kind of higher-order neutral functional differential equation with variable parameter

In this paper, we consider a kind of higher-order neutral equation with distributed delay and variable parameter: . By using the classical coincidence degree theory of Mawhin, sufficient conditions for the existence of periodic solutions are established. Recent results in the literature are generalized and significantly improved. Furthermore, two examples are given to illustrate that the results are almost sharp. MSC:34K10, 30D05, 34B45.

Global Existence Results for Neutral Functional Differential Equations with State-Dependent Delay

Our aim in this work is to study the existence of solutions of a neutral functional differential equation with state-dependent delay. We use the Schauder’s fixed point theorem to show the existence of global solutions.

Existence and uniqueness of periodic solutions for a system of nonlinear neutral functional differential equations with two functional delays

In this paper, we study the existence of periodic solutions of the nonlinear neutral system of differential equations $$\begin{aligned} \frac{d}{dt}x\left( t\right) =A\left( t\right) x\left( t-\tau \left( t\right) \right) +\frac{d}{dt}Q\left( t,x\left( t-g\left( t\right) \right) \right) +G\left( t,x\left( t\right) ,x\left( t-g\left( t\right) \right) \right) \!. \end{aligned}$$ By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. Our results extend and complement some earlier publications.

Neutral Functional Partial Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients

Neutral Functional Partial Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients

Controllability of impulsive neutral stochastic differential equations with fractional Brownian motion

In this paper, the controllability result of impulsive neutral stochastic functional differential equations with finite delay and fractional Brownian motion in a Hilbert space is studied. By using Banach's fixed point theorem, sufficient conditions are given for the controllability of the system. Finally, an example is given to illustrate the application of our result.

Neutral stochastic functional differential equations with infinite delay and Poisson jumps in the [formula omitted] space

In this paper, we prove the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay and Poisson jumps (INSFDEPs in short) in the phase space Cg with non-Lipschitz coefficients. Furthermore, we study the continuous dependence of the solution on the initial value by means of the corollary of the Bihari inequality.

Asymptotic stability of solution to nonlinear neutral and Volterra functional differential equations in Banach spaces

This paper is concerned with the asymptotic stability properties of the solution to nonlinear neutral and Volterra functional differential equations. Some sufficient conditions for the asymptotic stability of the systems are given. As an illustration of the applications of these investigations, the contractivity and asymptotic stability results of the solution to Volterra partial functional differential equations and delay integro-differential equations of “Hale’s” form are obtained respectively. These results form the basis for obtaining insight into the analogous properties of their numerical solutions.