Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces (original) (raw)

Controllability Results for Evolution Inclusions with Non-Local Conditions

Zeitschrift für Analysis und ihre Anwendungen, 2003

In this paper we prove controllability results for mild solutions defined on a compact real interval for first order differential evolution inclusions in Banach spaces with non-local conditions. By using suitable fixed point theorems we study the case when the multi-valued map has convex as well as non-convex values.

Approximate controllability of differential inclusions in Hilbert spaces

Nonlinear Analysis: Theory, Methods & Applications, 2012

In this paper controllability for the system originating from semilinear functional differential equations in Hilbert spaces is studied. We consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup, generated by the linear part of the inclusion, is compact and under the assumption that the corresponding linear system is approximately controllable. By using resolvent of controllability Gramian operator and fixed point theorem, sufficient conditions have been formulated and proved. Example is presented to illustrate the utility and applicability of the proposed method.

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2007

In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.

An existence result for impulsive functional differential inclusions in Banach spaces

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2004

We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces, moreover under some additional assumptions we prove the compactness of the solution set.

On semilinear differential inclusions in Banach spaces with nondensely defined operators

Journal of Fixed Point Theory and Applications, 2011

We consider a semilinear differential inclusion in a Banach space assuming that its linear part is a nondensely defined Hille-Yosida operator whereas Carathèodory-type multivalued nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We apply the theory of integrated semigroups and the fixed point theory of condensing multivalued maps to obtain local and global existence results and to prove the continuous dependence of the solutions set on initial data. An application to an optimization problem for a feedback control system is given.