Existence results for partial neutral functional integrodifferential equations with unbounded delay

We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray-Schauder alternative.     

Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces

In this work the controllability of fractional impulsive neutral functional integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, a semigroup of operators and Krasnoselskii’s fixed point theorem.     

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.     

Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces

In this paper sufficient conditions for the controllability of impulsive neutral integrodifferential systems with infinite delay are established. The results are obtained by using the Schauder fixed point theorem.     

Existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper is mainly concerned with the existence of solutions of first order nonlinear impulsive fractional integrodifferential equations in Banach spaces. The results are obtained by using fixed point principles. Further, some interesting examples are presented to illustrate the theory.     

Existence results for impulsive neutral evolution integrodifferential equations with infinite delay

In this paper we prove the existence of mild solutions for impulsive neutral evolution integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the analytic semigroup theory and the Krasnoselski–Schaefer type fixed point theorem. An example is provided to illustrate the theory.     

Existence of solutions of neutral functional integrodifferential equation in Banach spaces

In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space. The results are obtained by using the Schaefer fixed-point theorem.     

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

In this paper, we prove the controllability of second-order neutral functional differential inclusions in Banach spaces. The result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to Martelli.     

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

In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.     

On controllability of fractional impulsive neutral infinite delay evolution integrodifferential systems in Banach spaces

In this work, controllability of fractional impulsive neutral evolution integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, resolvent operators and Krasnoselskii’s fixed point theorem.     

Existence results for neutral functional differential inclusions in Banach algebras

In this paper an existence theorem for the first-order functional differential inclusions in Banach algebras is proved under the mixed generalized Lipschitz and Carathéodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.     

Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side

In this paper, Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo is used to investigate the existence of solutions for the first- and second-order functional and neutral functional integrodifferential inclusions with lower semicontinuous and nonconvex-valued right-hand side.     

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.     

Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay

In this paper we establish sufficient conditions for the approximate controllability of impulsive neutral functional evolution integrodifferential systems in Hilbert spaces. Also we study the exact controllability of the same system. The conditions are obtained by using Schauder’s fixed point theorem when the operator is compact and the Banach fixed point theorem when the operator is not compact. The results are obtained by using the evolution operators.     

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 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.     

Controllability of non-densely defined impulsive neutral functional differential systems with infinite delay in Banach spaces

In this paper, we investigate the controllability for a class of abstract impulsive neutral functional differential systems with infinite delay where the linear part is non-densely defined and satisfies the Hille–Yosida condition. The approach used is the Schauder fixed point theorem combined with the operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article.     

Impulsive neutral functional differential inclusions in Banach spaces

The aim of this paper is to study the existence of solutions to some classes of impulsive neutral functional differential inclusions in Banach spaces. We shall make use of a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler.     

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.     

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.