A note on controllability of semilinear integrodifferential systems in Banach spaces (Q1580053)

Semilinear integrodifferential dynamical systems with linear dependence on the controls are considered. A definition of exact controllability in a given time interval is presented. Using the Schaefer fixed point theorem, a sufficient condition for exact controllability is formulated and proved. In the proof several results taken from nonlinear functional analysis are used. Moreover, the paper contains several remarks and comments on the controllability problem for abstract nonlinear control systems. The relationships to the results existing in the literature are also given. Similar controllability problems for nonlinear control systems have been recently considered in the paper [\textit{K. Balachandran}, \textit{J. P. Dauer} and \textit{P. Balasubramaniam}, Controllability of nonlinear integrodifferential systems in Banach space, J. Optimization Theory Appl. 84, No. 1, 83-91 (1995; Zbl 0821.93010)].