Approximate controllability of semilinear functional equations in Hilbert spaces - Dauer, JP; Mahmudov, NI (Academic Press Inc Elsevier Science, 2002)
In this paper approximate and complete controllability for semilinear functional differential systems is studied in Hilbert spaces. Sufficient conditions are established for each of these types of controllability. The results address the limitation that linear systems in infinite-dimensional spaces with compact semigroup cannot be completely controllable. The conditions are obtained by using the Schauder fixed point theorem when the semigroup is compact and the Banach fixed point theorem when the semigroup is not compact. (C) 2002 Elsevier Science (USA). All rights reserved.
Keywords: approximate controllability; weak approximate controllability; complete controllability; semilinear functional equations; Schauder fixed point theorem; Banach fixed point theorem