About one strengthening of the Massera's existence theorem of periodic solutions of linear differential periodic systems (Q6581938)

The authors introduced a class of vector functions defined on the axis and called growing slower than a linear function. This class contains the class of bounded vector functions as its own subclass. It is proved that an ordinary differential non-homogeneous linear \(\omega\)-periodic system has an \(\omega \)-periodic solution if and only if it has a solution belonging to the introduced class. The proved assertion strengthens Massera's theorem.