Persistence and periodic solutions in systems of delay differential equations

Pablo Amster, Melanie Bondorevsky

Published 2020-01-31Version 1

We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence of non-trivial $T$-periodic solutions via topological degree techniques. Finally, we prove that, in some sense, the conditions are also necessary.