Controllability of second order semilinear delay integrodifferential systems in Banach spaces (Q2711265)

Semilinear, infinite-dimensional, second-order integrodifferential control systems, with distributed and point delays in the state variables are considered. Using the Schaefer fixed-point theorem, sufficient conditions for exact controllability in a given finite time interval are formulated and proved. In the proofs the theory of semigroups of linear operators is used. Several remarks and comments on the relationships between the results in the paper and those existing in the literature are presented. The Schaefer fixed-point theorem and the exact controllability definition are also recalled for the completeness of the considerations. Moreover, it should be pointed out that similar exact controllability problems for second-order infinite-dimensional control systems have been recently investigated in the paper [\textit{J. Y. Park} and \textit{H. K. Han}, Bull. Korean Math. Soc. 34, No. 3, 411-419 (1997; Zbl 0889.93008)].