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Periodic solutions and nontrivial periodic solutions for a class of Rayleigh-type equation with two deviating arguments. (English) Zbl 1292.34067

Summary: The Rayleigh equation with two deviating arguments \[ x''(t)+f(x'(t))+g_1(t,x(t-\tau_1(t)))+g_2(t,x(t-\tau_2(t)))=e(t) \] is studied. By using the Leray-Schauder index theorem and the 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.

MSC:

34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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