New results of periodic solutions for a class of delay Rayleigh equation

Abstract

In this studies, we discuss the following Rayleigh equation with two delays: $$ x''(t)+f(t,x'(t))+g_{1}(t,x(t-\tau_{1}))+g_{2}(t,x(t-\tau_{2}))=e(t). $$ By using Mawhin's continuation theorem and some new techniques, some criteria to guarantee the existence and uniqueness of periodic solutions of this equation is given. Our results are new and complement the known results in the literature.