Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity. (English) Zbl 1190.34050

Summary: It is proved that a periodically forced second-order equation with a singular nonlinearity in the origin with linear growth in infinity possesses a \(T\)-periodic stable solution for high values of the mean value of the forcing term. The method of proof combines a rescaling argument with the analysis of the first twist coefficient of the Birkhoff normal form for the Poincaré map.


34C25 Periodic solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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