Controllability problem of neutral equation with Nussbaum fixed-point theorem

The main objective of this article is to present the fixed-point theorem techniques for neutral equation. We consider an unconstrained controllability problem for semi linear stationary dynamical system. In the paper the appropriate hypotheses are presented. In the proof of the main results we use Nussbaum fixed-point theorem and solution of semi linear neutral equation. The main goal of the paper are the sufficient conditions for the relative controllability on the given time interval for studied dynamical system.