Controllability of nonlinear integrodifferential inclusions in Banach spaces with nonlocal conditions (Q2756994)

Nonlinear infinite-dimensional continuous-time control systems described by integrodifferential inclusions are considered. It is generally assumed that the system is semilinear, i.e., it contains both a linear and a nonlinear part. Moreover, the values of controls are unconstrained. Using a fixed point theorem for condensing maps [\textit{M. Martelli}, Boll. Unione Mat. Ital. (4) 11, Suppl. Fasc. 3, 70-76 (1975; Zbl 0314.47035)], sufficient conditions for exact controllability in a finite time interval are formulated and proved. In the proofs, methods of functional analysis are extensively used. As an application of the theoretical results, controllability conditions for a semilinear delay integrodifferential inclusion of Sobolev type are derived. Moreover, the paper contains several remarks and comments on the controllability of nonlinear infinite-dimensional control systems. Finally, it should be mentioned that similar controllability problems have been considered in the paper [\textit{K. Balachandran}, \textit{P. Balasubramaniam} and \textit{J. P. Dauer}, J. Optim. Theory Appl. 84, 83-91 (1995; Zbl 0821.93010)].