Impulsive Neutral Functional Differential Inclusions Research Articles

Existence results for quasilinear random impulsive abstract differential inclusions in Hilbert space

In this paper, the existence of solutions for quasilinear random impulsive neutral functional differential inclusions are studied for both convex and non-convex cases in a real separable Hilbert space. The results are obtained by using the Martelli, Covitz and Nadler’s fixed point theorems and semigroup theory. An example is given as an application for the abstract results.

Existence of Semi Linear Impulsive Neutral Evolution InclusionsWith Infinite Delay in Frechet Spaces

In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces

In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

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

In this paper, we investigate the existence of solutions for a class of second-order impulsive neutral functional differential inclusions in Banach spaces. Sufficient conditions for the existence are derived with the help of the fixed point theorem for multivalued maps due to Dhage.

Existence results for random impulsive neutral differential inclusions with lower semicontinuous

This article presents the results on existence of mild solutions for random impulsive neutral functional differential inclusions under sufficient conditions. The results are obtained by using the Krasnoselskii-Schaefer type fixed point theorem combined with the selection theorem of Berssan and Colombo for lower semicontinuous (LSC) maps with decomposable values.

Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

We investigate the controllability of impulsive neutral functional differential inclusions in Banach spaces. Our main aim is to find an effective method to solve the controllability problem of impulsive neutral functional differential inclusions with multivalued jump sizes in Banach spaces. Based on a fixed point theorem with regard to condensing map, sufficient conditions for the controllability of the impulsive neutral functional differential inclusions in Banach spaces are derived. Moreover, a remark is given to explain less conservative criteria for special cases, and work is improved in the previous literature.

Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay

This paper is concerned with controllability of a partial neutral functional differential inclusion of second order with impulse effect and infinite delay. We introduce a new phase space to prove the controllability of an inclusion which consists of an impulse effect with infinite delay. We claim that the phase space considered by different authors is not correct. We establish the controllability of mild solutions using a fixed point theorem for contraction multi-valued maps and without assuming compactness of the family of cosine operators.

Existence results for second-order impulsive neutral functional differential inclusions in Banach spaces

In this paper, we investigate the existence of mild solutions on a compact interval to second-order impulsive neutral functional differential inclusions in Banach spaces. The results are obtained by using the theory of continuous cosine families and a fixed point theorem due to Dhage.

Existence of random impulsive abstract neutral non-autonomous differential inclusions with delays

This article presents the results on existence of mild solutions of random impulsive neutral functional differential inclusions under sufficient conditions. The results are obtained by using the Dhage’s fixed point theorem.

Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay

This paper deals with the controllability of a class of impulsive neutral stochastic functional differential inclusions with infinite delay in an abstract space. Sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multi-valued operators due to Dhage. An example is provided to illustrate the obtained theory.

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 results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions

According to theories for integrated semigroups and Leray-Schauder theorem of the alternative for Kakutani maps, this paper is mainly concerned with existence results for some non-densely defined impulsive neutral functional differential inclusions with nonlocal conditions in Banach spaces. An example is also given to illustrate the obtained theorem.

A second-order multivalued boundary-value problem and impulsive neutral functional differential inclusions in Banach spaces

In this paper, by using the new fixed-point theorem of O'Regan and Precup and a noncompact measure, we study the existence of solutions of a second-order multivalued boundary-value problem in Banach spaces and the existence of a mild solution for impulsive neutral functional differential inclusions in Banach spaces. The compactness conditions and the upper-semicontinuity conditions for multivalued integral operators are weakened in this paper.

Second Order Impulsive Neutral Functional Differential Inclusions

Abstract. In this paper, we investigate the existence of solutions of second order im-pulsive neutral functional differential inclusions which the nonlinearity F admits convexand non-convex values. Some results under weaker conditions are presented. Our resultsextend previous ones. The methods rely on a fixed point theorem for condensing mul-tivalued maps and Schaefer’s fixed point theorem combined with lower semi-continuousmultivalued operators with decomposable values. 1. IntroductionIn this paper, we consider the existence results of solutions for the followingsecond-order neutral functional differential inclusions with the form(1.1)p(t)u 0 (t)−Z tt−τ q(s)u(s)ds 0 ∈ F(t,u t ), a.e.t∈ [0,T]\{t 1 ,t 2 ,··· ,t m },(1.2) ∆u| t=t k = I k (u(t −k )), ∆u 0 | t=t k = J k (u(t −k )), k= 1,2,··· ,m,(1.3) u(t) = a(t),t∈ [−τ,0],u 0 (0) = η,where F: [0,T] × C→ P(R n ) is a multi-valued map, C= {ϕ : [−τ,0] → R ; ϕis continuous everywhere except for a finite number of points ˜tat which ϕ(˜t − ) andϕ(˜t

Solvability of impulsive neutral functional differential inclusions in banach spaces

Impulsive neutral differential inclusions play an important role in characterizing many social, physical and engineering problems, and the existence of solutions for the initial value problem in Banach spaces has been extensively studied. However, in most cases, the nonlinear term on the right-hand side of differential inclusions has to satisfy the compact or continuous assumptions. The object of this paper is to study the existence of solutions to the initial value problems of the first and second order impulsive neutral functional differential inclusions in Banach spaces under some weaker conditions, where the nonlinear term on the right-hand side does not necessarily satisfy the compact and continuous assumptions. Based on a fixed point theorem for discontinuous multivalued increasing operators, the results are obtained by means of the partial ordering method and measure of noncompactness.

Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces

In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage’s fixed point theorem.

Existence for neutral impulsive differential inclusions with nonlocal conditions

In this paper, by using a fixed point theorem for condensing multi-valued maps, we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions. As an application, an example has been presented to illustrate the results obtained.

A comment on the papers: Controllability results for functional semilinear differential inclusions in Fréchet spaces [Nonlinear Anal. 61 (3) (2005) 405–423] and Controllability of impulsive neutral functional differential inclusions with infinite delay [Nonlinear Anal. 60 (8) (2005) 1533–1552

In this note we make some observations relating two papers recently published in Nonlinear Analysis Theory, Methods & Applications.

Existence results for impulsive neutral functional differential inclusions

In this paper we prove existence results for first and second order impulsive neutral functional differential inclusions under the mixed Lipschitz and Caratheodory conditions.

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.