The Rayleigh equation with two deviating arguments x′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t) is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results.
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