Periodic solutions of some nonlinear autonomous functional differential equations

Abstract

We develop here some new fixed point theorems and apply them to the question of existence of nontrivial periodic solutions of nonlinear, autonomous functional differential equations. We prove that the standard results of G. S. Jones and R. B. Grafton can be obtained by our methods, and we prove periodicity results for some equations, for instance a neutral functional differential equation, which appear inaccessible by previous techniques.