On the Exact Global Controllability of a Semilinear Evolution Equation

For the Cauchy problem associated with a controlled semilinear evolution equation withan operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exactcontrollability into a given terminal state (and also into given intermediate states at interim timemoments) on an arbitrarily fixed (without additional constraints) time interval. Here we use theBrowder—Minty theorem and also a chain technology of successive continuation of the solution ofthe controlled system to intermediate states. As examples, we consider a semilinearpseudoparabolic equation and a semilinear wave equation.