A priori bounds for periodic solutions of a delay Rayleigh equation. (English) Zbl 0980.34068

Consider the delay equation \((*)\) \(x'' (t) + \lambda f(x' (t)) + \lambda g(x(t-\tau (t))) =\lambda p(t),\) where all functions are continuous, \(\tau\) and \(p\) are \(2\pi\)-periodic, \(f(0)=0.\) The authors establish a priori bounds on periodic solutions to \((*)\) and prove a theorem on the existence of periodic solutions by means of the continuation method.


34K13 Periodic solutions to functional-differential equations
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