Impulsive semilinear neutral functional differential inclusions with multivalued jumps

In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.     

Solvability of impulsive neutral evolution differential inclusions with state-dependent delay

In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has sub-linear growth in the state variable.     

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.     

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 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 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.     

Existence results for some partial functional differential equations with state-dependent delay

In this paper, we establish sufficient conditions for the existence of solutions for some partial functional differential equations with state-dependent delay; we assume that the linear part is not necessarily densely defined and satisfies the well-known Hille–Yosida conditions. Our approach is based on a nonlinear alternative of Leray–Schauder type and integrated semigroup theory. An application is provided to a reaction–diffusion equation with state-dependent delay.     

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

In this paper we study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay.     

Existence and controllability results for impulsive partial functional differential inclusions

In this paper we prove the existence and the controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions.     

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.     

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.     

Approximate controllability of second-order impulsive stochastic differential equations with state-dependent delay

In this paper we study a kind of second-order impulsive stochastic differential equations with state-dependent delay in a real separable Hilbert space. Some sufficient conditions for the approximate controllability of this system are formulated and proved under the assumption that the corresponding deterministic linear system is approximately controllable. The results concerning the existence and approximate controllability of mild solutions have been addressed by using strongly continuous cosine families of operators and the contraction mapping principle. At last, an example is given to illustrate the theory.     

Existence of solutions for impulsive partial neutral functional differential equation with infinite delay

In this paper, the existence of mild solutions for first-order impulsive semilinear neutral functional differential equations with infinite delay in Banach spaces is investigated. We derive conditions in respect of the Hausdorff measure of noncompactness under which the mild solutions exist in Banach spaces. Our results improve and generalize some previous results.     

Existence results for a nondensely-defined impulsive neutral differential equation with state-dependent delay

In this paper, we prove the existence of integral solutions for a first order nondensely-defined impulsive neutral differential equation with state-dependent delay. The results are obtained by using suitable fixed point theorems. As applications of these main theorems, some consequences are obtained for the sub-linear growth cases.     

On state-dependent delay partial neutral functional integro-differential equations

In this paper the existence of mild solutions for a class of abstract neutral integro-differential equations with state-dependent delay is studied.     

On a fractional impulsive partial stochastic integro-differential equation with state-dependent delay and optimal controls

This paper is mainly concerned with a new class of fractional impulsive partial stochastic integro-differential equations with state-dependent delay and optimal controls in Hilbert spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence and uniqueness of mild solutions are proved by means of stochastic analysis theory, fractional calculus and the fixed point technique combined with solution operator. The existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. Finally, an example is given for demonstration.     

Solvability of nonlinear impulsive Volterra integral inclusions and functional differential inclusions

This paper presents sufficient conditions for the existence of solutions to nonlinear impulsive Volterra integral inclusions and initial value problems for second order impulsive functional differential inclusions in Banach spaces. Our results are obtained via a fixed point theorem due to Hong [J. Math. Anal. Appl. 282 (2003) 151-162] for discontinuous multivalued increasing operators.     

Stability of differential inclusions with multivalued perturbations

Translated from Matematicheskie Zametki, Vol. 43, No. 3, pp. 346–355, March, 1988.     

On nonresonance impulsive functional differential inclusions with nonconvex valued right-hand side

In this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions. We shall rely on the Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued maps with nonempty closed and decomposable values.