RECENT RESULTS ON PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS

Abstract

This chapter presents some recent results on periodic solutions of differential equations. The use of functional analytic methods in the study of periodic solutions or of boundary value problems for ordinary or functional differential equations has been extensively developed in the past few years. In particular, degree arguments have been systematically used to give simple and unified proofs of a number of existence theorems. The chapter presents a survey of recent theorems that, even if their original proof is quite different, fall into the scope of coincidence degree theory, especially the corresponding continuation theorem. As for the usual Leray–Schauder continuation theorem, the more difficult point in applying the result is to obtain a priori estimates for the possible solutions. Coincidence degree approach can also be used to extend and simplify considerably the treatment of some old and recent perturbations type results for periodic solutions of differential equations.