23 research outputs found
Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions
In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness
The Kneser property for abstract retarded functional differential equations with infinite delay
We establish existence of mild solutions for a class of
semilinear first-order abstract retarded functional differential
equations (ARFDEs) with infinite delay and we prove
that the set consisting of mild solutions for this problem is
connected in the space of continuous functions
Impulsive partial neutral differential equations
AbstractIn this work we study the existence and regularity of mild solutions for impulsive first order partial neutral functional differential equations with unbounded delay
Existence results for fractional integro-differential inclusions with state-dependent delay
In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given
Controllability and stabilizability of linear time-varying distributed hereditary control systems
This paper is concerned with the controllability and stabilizability problem for control systems described by a time-varyinglinear abstract differential equation with distributed delay in the state variables. An approximate controllability propertyis established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operatorsassociated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptoticstability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximatecontrollability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes thesystem. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley &Sons, Ltd