Unbounded Continuum of Periodic Solutions for Autonomous Delay Equations

This work is devoted to the study of the existence of an unbounded continuum of periodic solutions that appear by Hopf bifurcation in non-linear delay differential equations. Our main objective is to give a theorem that guarantees the appearance of an unbounded continuum of periodic solutions. Furthermore, the verification of the hypotheses requires much less effort than the known results in the literature. In the last section some applications to examples already studied show the power of the theorem.