Periodic solutions in ordinary differential equations using dissipativity conditions (Q2367668)

The author studies the existence and uniqueness of periodic solutions for equations of the form \(\dot X= f(t,X)\). The proofs depend on dissipativity conditions for some equations related to that equation by the Leray-Schauder continuation principle. A modification and partial improvement of the assumptions considered in a previous paper of another author is proposed in order to provide a correction of the corresponding results. Applications with a counterexample are developed.