A study on approximate controllability of linear impulsive equations in Hilbert spaces (Q6618740)

The approximate controllability for an impulsive linear evolution system in Hilbert spaces is investigated in this paper. The explicit representation of solution in terms of semigroup and impulsive operators is presented. The necessary and sufficient conditions for approximate controllability in terms of resolvent operators are established. The results in this paper will bring new theories to readers who will be intested in this topic. The efficiency of such findings can be well extended to approximate controllability with various impulsive fractional linear/semilinear differential structures.