Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity

Pedro J. Torres a1
a1 Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain (

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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.

(Published Online February 9 2007)
(Received June 6 2005)
(Accepted January 25 2006)