## 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.

### MSC:

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