Neutral Functional Differential Equations Research Articles

Existence and Stability Results of Impulsive Stochastic Partial Neutral Functional Differential Equations with Infinite Delays and Poisson Jumps

In this paper, we are focused upon the results on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations with infinite delays and poisson jumps. The results are obtained by using the method of successive approximation and Bihari’s inequality.

Moderate deviations for neutral functional stochastic differential equations driven by Lévy noises

Using the weak convergence method introduced by A. Budhiraja, P. Dupuis, and A. Ganguly [Ann. Probab., 2016, 44: 1723–1775], we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.

Asymptotic behavior of solutions of nonautonomous neutral dynamical systems

This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the trajectories of problems described by this kind of equations, such us compartmental systems and neural networks among many others. Precisely, more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non-neutral part.

Asymptotic Stability of Neutral Set-Valued Functional Differential Equation by Fixed Point Method

This paper studies a class of nonlinear neutral set-valued functional differential equations. The globally asymptotic stability theorem with necessary and sufficient conditions is obtained via the fixed point method. Meanwhile, we give an example to illustrate the obtained result.

Three positive periodic solutions of second order nonlinear neutral functional differential equations with delayed derivative

This paper deals with the existence of three positive periodic solutions for a class of second order neutral functional differential equations involving the delayed derivative term in nonlinearity (x(t)-cx(t-delta)){''}+a(t)g(x(t))x(t)=lambda b(t)f(t,x(t),x(t-tau_{1}(t)),x'(t-tau_{2}(t))). By utilizing the perturbation method of positive operator and Leggett–Williams fixed point theorem, a group of sufficient conditions are established.

Convergence in a system of critical neutral functional differential equations

In this study, we investigate the dynamic behavior on a system of neutral functional differential equations in critical case. Combining monotonicity techniques and functional methods, we develop the delicate monotonicity with the addressed system and show the convergence for every pre-compact solution with some initial condition, which improves and complements some existing ones.

Averaging principle for neutral stochastic functional differential equations with impulses and non-Lipschitz coefficients

In this paper, we consider the stochastic periodic averaging principle for impulsive neutral stochastic functional differential equations with non-Lipschitz coefficients. By using the theory of stochastic analysis and elementary inequalities, we show that the solutions of impulsive neutral stochastic functional differential equations converge to the solutions of the corresponding averaged neutral stochastic functional differential equations without impulses.

Periodic Solutions to Partial Neutral Functional Differential Equations in Admissible Spaces on a Half-Line

We prove the existence and uniqueness of periodic solutions to partial neutral function differential equation of the form $\frac {\partial Fu_{t}}{\partial t}= A(t)Fu_{t} +g(t,u_{t}),~t\in [0,\infty )$, on a Banach space X, where the operator-valued function t↦A(t) and the nonlinear delay operator g(t,v) are both T-periodic with respect to t, whereas g is φ-Lipschitz with respect to v for φ belonging to an admissible space. Then, in the case that the family (A(t))t≥ 0 generates an evolution family having an exponential dichotomy, we apply our abstract results to study the existence, uniqueness of periodic solutions. We also prove the conditional stability, and the existence of local stable manifolds around such periodic solutions.

Normal Forms for Partial Neutral Functional Differential Equations with Applications to Diffusive Lossless Transmission Line

A class of partial neutral functional differential equations are considered. For the linearized equation, the semigroup properties and formal adjoint theory are established. Based on these results, we develop two algorithms of normal form computation for the nonlinear equation, and then use them to study Hopf bifurcation problems of such equations. In particular, it is shown that the normal forms, derived from these two different approaches, for the Hopf bifurcation are exactly the same. As an illustration, the diffusive lossless transmission line equation where a Hopf singularity occurs is studied.

Stability of a Class of Impulsive Neutral Stochastic Functional Partial Differential Equations

In this paper, a class of impulsive neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion is investigated. Under some suitable assumptions, the pth moment exponential stability is discussed by means of the fixed-point theorem. Our results also improve and generalize some previous studies. Moreover, one example is given to illustrate our main results.

Large deviations for neutral stochastic functional differential equations

In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential equations.

On a symbolic method for neutral functional-differential equations with proportional delays

In this paper, we present a new symbolic method for solving neutral functional-differential equations with proportional delays having variable coefficients via homotopy perturbation method. The pro...

Inertial manifolds for neutral functional differential equations with infinite delay and applications

Inertial manifolds for neutral functional differential equations with infinite delay and applications

Sensitivity to small delays of mean square stability for stochastic neutral evolution equations

In this work, we are concerned about the mean square exponential stability property for a class of stochastic neutral functional differential equations with small delay parameters. Both distributed and point delays under the neutral term are considered. Sufficient conditions are given to capture the exponential stability in mean square of the stochastic system under consideration. As an illustration, we present some practical systems to show their exponential stability which is not sensitive to small delays in the mean square sense.

Existence of nonoscillatory solutions for fractional neutral functional differential equation

Existence of nonoscillatory solutions for fractional neutral functional differential equation

Stability by the First Approximation of a Water Hammer Model

Abstract Usually the water hammer models in hydroelectric engineering are described by the adapted Saint-Venant Partial Differential Equations with linear and nonlinear boundary conditions. If the dynamic head and the Darcy-Weisbach losses are neglected the PDEs are linear hyperbolic and can be tackled by associating a system of Neutral Functional Differential Equations with two delays - there are two conduits (the tunnel and the penstock). The time scale analysis shows that in certain cases arising from practice the dynamics of the penstock can be considered as described by ordinary differential equations. Consequently the water hammer dynamics has now a single time delay. The stability is then discussed by analyzing the characteristic equation: frequency domain methods combined with algebraic ones are implied. In this way stability by the first approximation is obtained. From the engineering point of view the results display the stabilizing role of the surge tank.

Existence, uniqueness and stability of impulsive stochastic neutral functional differential equations driven by Rosenblatt process with varying-time delays

Abstract Hermite processes are self-similar processes with stationary increments; the Hermite process of order 1 is fractional Brownian motion (fBm) and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of impulsive neutral stochastic functional differential equations with variable delays driven by Rosenblatt process with index {H\in(\frac{1}{2},1)} , which is a special case of a self-similar process with long-range dependence. More precisely, we prove an existence and uniqueness result, and we establish some conditions, ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

Existence results for systems of coupled impulsive neutral functional differential equations driven by a fractional Brownian motion and a Wiener process

Abstract In this paper, we prove some results on the existence and uniqueness of mild solutions for a system of semilinear impulsive differentials with infinite fractional Brownian motions and a Wiener process. Our approach is based on a new version of fixed point theorem, due to Krasnoselskii, in generalized Banach spaces.

Positive periodic solutions for neutral functional differential equations

In this paper, we investigate the existence of positive periodic solution for the first order neutral differential equation. The results are established using a fixed point theorem in cones of Banach space.

Oscillation criteria for second-order quasi-linear neutral functional differential equation

In this work, new sufficient conditions for oscillation of solution of second order neutral delay differential equation are established. One objective of our paper is to further simplify and complement some results which were published lately in the literature. In order to support our results, we introduce illustrating examples.