Existence of Periodic Solutions for a Semilinear Ordinary Differential Equation
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Dancer  found a necessary and sufficient condition for the existence of periodic solutions to the equation x¨ + g1 (x˙) + g0(x) = f (t) His condition is based on a functional that depends on the solution to the above equation with g0 = 0. However, that solution is not always explicitly known which makes the condition unverifiable in practical situations. As an alternative, we find computable bounds for the functional that provide a sufficient condition and a necessary condition for the existence of solutions.