Semilinear Functional Differential Inclusions Research Articles

A Controllability Problem for Causal Functional Inclusions with an Infinite Delay and Impulse Conditions

In this paper we study the controllability problem in a Banach space for various classes of functional inclusions with causal operators with an infinite delay, and impulse effects. Basing on the topological degree theory for condensing multimaps, we prove a global theorem on the existence of trajectories for systems governed by functional inclusions. As an application, we obtain generalizations of existence theorems for the controllability problem for a semilinear first order functional differential inclusions of this type and a semilinear functional differential inclusions of a fractional order 0 < q < 1.

Viability result for semilinear functional differential inclusions in Banach spaces

We show the existence result of a mild solution for a semilinear functional differential inclusion, with viability, governed by a family of linear operators. We consider the case when the constraint is moving.

Finite-time attractivity for semilinear functional differential inclusions

Our aim in this paper is to analyze a sufficient condition ensuring the finite-time attractivity for the solutions to semilinear functional differential inclusions in Banach spaces. The obtained results will be applied to a class of partial differential equations.

Existence for Impulsive Semilinear Functional Differential Inclusions

In this paper we investigate the existence of solutions for first-order impulsive semilinear functional differential inclusions in Banach spaces. Sufficient condition for the existence is obtained with the well-known Covitz and Nadler’s fixed point theorem for multivalued contractions.

Finite-time attractivity of solutions for a class of fractional differential inclusions with finite delay

Our aim in this paper is to give a sufficient condition ensuring the finite-time attractivity for the zero solution to semilinear functional differential inclusions in Banach spaces, in the case where the nonlinearity function possibly has superlinear growth. Our analysis is based on the semigroup theory, the fixed point principle for condensing multi-valued maps, and local estimates of solutions. The abstract results will be applied to a class of polytope inclusions in $$C_0$$ setting.

Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures

A second order semilinear impulsive functional differential inclusion in a separable Hilbert space is considered. Without imposing hypotheses of the compactness on the cosine families of operators, some sufficient conditions of approximate controllability are formulated in the case where the multivalued nonlinearity of the inclusion is a completely continuous map dominated by a function. By the use of resolvents of controllability Gramian operators and developing appropriate computing techniques for the Hausdorff product measures of noncompactness, the results of approximate controllability for position and velocity are derived. An example is also given to illustrate the application of the obtained results.

Controllability for noninstantaneous impulsive semilinear functional differential inclusions without compactness

The first part of this paper considers the controllability for a functional semilinear differential inclusion governed by a family of operators {A(t):t∈[0,b]} generating an evolution operator in a Banach space in the presence of noninstantaneous impulse effects. In the second part of this paper we study the controllability for a fractional noninstantaneous impulsive semilinear differential inclusion with delay, where the linear part is an infinitesimal generator of a C0−semigroup. Using a weakly convergent criterion in the space of piecewise continuous functions and weak topology theory (for weak sequentially closed graph operators) we establish sufficient conditions to guarantee controllability results. Examples are given to illustrate the abstract results.

Controllability results for second order semilinear functional differential inclusions based on Kuratowski product measures

Controllability results for second order semilinear functional differential inclusions based on Kuratowski product measures

Hausdorff product measures and $C^1$-solution sets of abstract semilinear functional differential inclusions

A second order semilinear neutral functional differential inclusion with nonlocal conditions and multivalued impulse characteristics in a separable Banach space is considered. By developing appropriate computing techniques for the Hausdorff product measures of noncompactness, the topological structure of $C^1$-solution sets is established; and some interesting discussion is offered when the multivalued nonlinearity of the inclusion is a weakly upper semicontinuous map satisfying a condition expressed in terms of the Hausdorff measure.

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.

On The Exact Controllability of Impulsive Fractional Semilinear Functional Differential Inclusions

AbstractIn this paper, we deal with the exact controllability for impulsive fractional semilinear functional differential inclusions in Hilbert spaces. Under suitable assumptions, the exact controllability of the control systems are formulated and proved. The main tools in our study rely on the fixed point theorem for multivalued maps due to Dhage associated with evolution systems.

Задача управляемости для импульсных полулинейных вырожденных функционально-дифференциальных включений с бесконечным запаздыванием

Задача управляемости для импульсных полулинейных вырожденных функционально-дифференциальных включений с бесконечным запаздыванием

Existence and controllability results for some impulsive partial functional differential inclusion

In this work, we prove the existence of mild and extremal mild solutions for first-order semilinear non densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions. Firstly, we show the existence of mild and extremal solutions. Secondly, we study the controllability of a semilinear functional differential inclusions.

Existence results on random impulsive semilinear functional differential inclusions with delays

This article presents the result on existence of mild solutions for random impulsive semilinear functional dierential inclusions under sucient conditions. The results are obtained by using the Martelli xed point theorem and the xed point theorem due to Covitz and Nadler.

On certain classes of functional inclusions with causal operators in Banach spaces

We introduce the notion of a multivalued causal operator and consider an abstract Cauchy problem in a Banach space for various classes of functional inclusions with causal operators. The methods of the topological degree theory for condensing maps are applied to obtain local and global existence results for this problem and to study the continuous dependence of a solution set on initial data. As application we generalize some existence results for semilinear functional differential inclusions and Volterra integro-differential inclusions with delay.

Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and on the jump functions. As example, we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.

Nonlinear impulsive partial functional differential inclusions with state-dependent delay and multivalued jumps

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined impulsive semilinear functional differential inclusions with state-dependent delay in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators.

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.

Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions

In this paper, we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators. The question of controllability of these equations and the topological structure of the solutions set are considered too.