Impulsive Neutral Functional Differential Equations Research Articles

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.

Asymptotic Stability of Stochastic Impulsive Neutral Partial Functional Differential Equations

In this paper the authors study the existence and asymptotic stability in p-th moment of mild solutions to stochastic neutral partial differential equation with impulses. Their method for investigating the stability of solutions is based on the fixed point theorem.

Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations

The existence of piecewise almost periodic solutions for impulsive neutral functional differential equations in Banach space is investigated. Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory.

A note on exponential stability for impulsive neutral stochastic partial functional differential equations

In this note, the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique. Some sufficient conditions are established for the concerned problem, and some existing results are generalized and improved. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

Existence of solutions for fractional impulsive neutral functional differential equations with infinite delay

In this paper, we first introduce a class of impulsive neutral fractional functional differential equations which arise from many practical applications such as in viscoelasticity and electrochemistry. After providing a natural formula of solutions for the equations, we then give an existence theorem of the solutions by using the Hausdorff's measure of noncompactness and the theory of Mönch. As a result, the existence theory provides a theoretical basis for exploring the solutions of such kinds of differential equations.

Approximate Controllability of Impulsive Neutral Functional Differential Equations with State-dependent Delay via Fractional Operators

In this article, the problem of approximate controllability for nonlinear impulsive neutral differential systems with state-dependent delay is studied under the assumption that the corresponding linear control system is approximately controllable. Using Schauder’s fixed point theorem and fractional powers of operators with semigroup theory, sufficient conditions are formulated and proved.

Existence results for nondensely defined impulsive neutral functional differential equations with infinite delay

In this paper, we study a class of impulsive neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille–Yosida theorem. We give some sufficient conditions ensuring the existence of integral solutions and strict solutions. To illustrate our abstract results, we conclude this work with an example.

Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered.

Mild solutions for impulsive neutral functional differential equations with state-dependent delay

In this work, we establish the existence of mild solutions for a class of impulsive neutral functional differential equations with state-dependent delay.

The existence of solutions for impulsive neutral functional differential equations

This work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed (not necessarily bounded) operators { A ( t ) : t ∈ I } .

Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

Existence results for a second order impulsive functional differential equation with state-dependent delay

In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical consequences are derived for the sub-linear growth cases. And an example is also given to illustrate our main results.

Existence results for impulsive neutral functional differential equations with state-dependent delay

In this article, we study the existence of mild solutions for a class of impulsive abstract partial neutral functional differential equations with state-dependent delay. The results are obtained by using Leray-Schauder Alternative fixed point theorem. Example is provided to illustrate the main result.

Controllability of second-order impulsive neutral functional differential inclusions in Banach spaces

In this paper, we shall prove the controllability of second-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multi-valued mappings. As an example, we also consider an second-order impulsive neutral functional differential equation with infinite delay. Copyright © 2009 John Wiley & Sons, Ltd.

Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions

The existence, uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal Cauchy problem in general Banach spaces are studied, by using the fixed point technique and semigroup of operators.

Existence results for impulsive neutral functional differential equations with infinite delay

In this work, we prove the existence of mild solutions for impulsive partial neutral functional differential equations with infinite delay in a Banach space. The results are obtained by using the Krasnoselski–Schaefer type fixed point theorem.

Existence results for an impulsive neutral functional differential equation with state-dependent delay

In this article, we study the existence of mild solutions for a class of impulsive abstract partial neutral functional differential equations with state-dependent delay. The results are obtained by using Leray–Schauder Alternative fixed point theorem.

Controllability of impulsive neutral functional differential inclusions with infinite delay

The paper is concerned with the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in a Banach space. Sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to Martelli. As an application, we also consider an impulsive neutral partial functional differential equation.

Multiple solutions for impulsive semilinear functional and neutral functional differential equations in Hilbert space

The well-known Krasnoselskii twin fixed point theorem is used to investigate the existence of mild solutions for first- and second-order impulsive semilinear functional and neutral functional differential equations in Hilbert spaces.

Impulsive neutral functional differential equations with variable times

In this paper, a fixed point theorem due to Schaefer is used to investigate the existence of solutions for first and second order impulsive neutral functional differential equations with variable times.