On impulsive functional differential inclusions with Hille-Yosida operators in Banach spaces

We consider a semilinear functional differential inclusion with infinite delay and impulse characteristics in a Banach space assuming that its linear part is a non-densely defined Hille-Yosida operator. We assume that the multivalued nonlinearity of upper Carathèodory or almost lower semicontinuous type satisfies a regularity condition expressed in terms of the measures of noncompactness. We apply the theory of integrated semigroups and the theory of condensing multivalued maps to obtain local and global existence results. The application to an optimization problem for an impulsive feedback control system is given.     

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.     

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 ABSTRACT RETARDED FUNCTIONAL DIFFERENTIAL SYSTEMS WITH INFINITE DELAY

This paper is concerned with the controllability of retarded functional differential systems with infinite delay in a general Banach space, via a fixed point approach. Sufficient conditions for controllability are established by using the Leray-Schauder alternative. An example is given to illustrate the results.     

Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space

In this paper, sufficient conditions are given for the controllability of a class of partial stochastic functional differential inclusions with infinite delay in an abstract space with the help of the Leray-Schauder nonlinear alternative. An example is provided to illustrate the theory.     

Controllability for Neutral Stochastic Functional Integrodifferential Infinite Delay Systems in Abstract Space

In this paper, sufficient conditions are given for the controllability of a class of neutral stochastic functional integrodifferential equations with infinite delay in abstract space. The Nussbaum fixed point theorem is adapted to obtain the controllability results, which greatly extends the previous results to the stochastic settings with the help of analytic semigroups. An example is provided to illustrate the theory.     

Controllability of Nonlinear Neutral Evolution Integrodifferential Systems with Infinite Delay

Sufficient conditions are derived for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in a Banach space. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An example is given to illustrate the results.     

Controllability of Neutral Functional Differential and Integrodifferential Inclusions with Infinite Delay

Sufficient conditions are derived for the controllability of neutral functional differential and integrodifferential inclusions with infinite delay in a Banach space. The results are obtained by using a fixed-point theorem for condensing maps due to Martelli. An example is given to illustrate the results.     

Measure functional differential equations with infinite delay

We introduce measure functional differential equations with infinite delay and an axiomatically described phase space. We show how to transform these equations into generalized ordinary differential equations whose solutions take values in a suitable infinite-dimensional Banach space. Even in the special case of functional equations with finite delay, our result improves the existing one by imposing weaker conditions on the right-hand side.     

Controllability of nonlinear third order dispersion equation with distributed delay

This paper is concerned with the exact controllability of nonlinear third order dispersion equation with infinite distributed delay. Sufficient conditions are formulated and proved for the exact controllability of this system. Without imposing a compactness condition on the semigroup, we establish controllability results by using a fixed point analysis approach.     

二阶非线性中立型无限时滞随机微分包含的可控性

本文主要在希尔伯特空间中讨论了二阶非线性中立型无限时滞随机微分包含的可控性问题.利用凝聚不动点定理得到了系统可控的一个充分性条件.     

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

The paper establishes a sufficient condition for the controllability of the first-order impulsive functional differential systems with infinite delay in Banach spaces. We use Schauder’s fixed point theorem combined with a strongly continuous operator semigroup. An example is given to illustrate our results.     

Representation of solutions and stability of linear differential-difference equations in a Banach space

In this paper the theory of linear delay differential equations is extended in three directions. One, the underlying phase space is allowed to be a Banach space so that equations with unbounded operators may be considered. Two, the delay is permitted to be effective over an infinite interval and a connection is made between this type of system and neutral systems whose delay is effective over a finite interval. Three, a theory of uniform asymptotic stability for linear delay differential equations in a Hilbert space is developed.     

Relative approximate controllability of abstract functional systems with infinite delay and delayed control

This paper is concerned with the relative approximate controllability of functional systems with infinite delay and delayed control in Hilbert spaces. In particular, we begin with studying some criteria of the controllability of linear systems. Based on those results, sufficient conditions are derived for the relative approximate controllability of nonlinear functional systems. Finally, an example is included to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

On the dynamics of equations with infinite delay

We consider a system of ordinary differential equations with infinite delay. We study large time dynamics in the phase space of functions with an exponentially decaying weight. The existence of an exponential attractor is proved under the abstract assumption that the right-hand side is Lipschitz continuous. The dimension of the attractor is explicitly estimated. Research supported by the project LC06052 of the Czech Ministry of Education.     

The Dissipation Inequality for Differential-Algebraic Systems

We discuss the infinite time-horizon linear-quadratic optimal control problem for differential-algebraic equations. In contrast to previous approaches we do not impose any assumptions on the system except for impulse controllability. In particular, we show that the optimal control problem is feasible if and only if a dissipation inequality has a solution. Moreover, we discuss conditions under which the problem has a minimizing (instead of only an infimizing) solution and furthermore, when this minimizing solution is unique. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Almost automorphy for abstract neutral differential equations via control theory

In this paper we study the existence of almost automorphic solutions for a class of linear neutral functional differential equations with finite delay and values in a Banach space. We show that the existence of an almost automorphic mild solution is related to the approximate controllability of a distributed control system. We applied our results to establish the existence of an almost automorphic solution for a neutral wave equation with delay.     

In memore of E.M. Landis

The purpose of this paper is to establish local theory for retarded functional differential equations with infinite delay, Some new conditions are proposed, and new results are obtained which is more general than the previous one. Our phase space is pseudo-metric space. We do not need x₊ to be continuous in t on phase space. Our theorems are especially effective for Volterra integro-differential equations     

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system.