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
ẍ + g1 (ẋ) + g0(x) = ƒ(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.
CitationGirg, P. (1998). Existence of periodic solutions for a semilinear ordinary differential equation. Electronic Journal of Differential Equations, 1998(31), pp. 1-10.
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