On the Exact Controllability of a Semilinear Evolution Equation with an Unbounded Operator

For the Cauchy problem associated with a controlled semilinear evolution equation withan unbounded maximal monotone operator in a Hilbert space, sufficient conditions are obtainedfor exact controllability to a given final state. Here a generalization of the Browder-Mintytheorem and results on the total global solvability of this equation obtained by the author earlierare used. As an example, a semilinear wave equation is considered.