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Approximate controllability of some nonlinear systems in Banach spaces

Nazim I Mahmudov

Author Affiliations

Eastern Mediterranean University, via Mersin 10, Famagusta, T.R. North Cyprus, Turkey

Boundary Value Problems 2013, 2013:50  doi:10.1186/1687-2770-2013-50

Published: 13 March 2013


In this paper, abstract results concerning the approximate controllability of semilinear evolution systems in a separable reflexive Banach space are obtained. An approximate controllability result for semilinear systems is obtained by means of Schauder’s fixed-point theorem under the compactness assumption of the linear operator involved. It is also proven that the controllability of the linear system implies the controllability of the associated semilinear system. Then the obtained results are applied to derive sufficient conditions for the approximate controllability of the semilinear fractional integrodifferential equations in Banach spaces and heat equations.