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

Published online by Cambridge University Press:  09 February 2007

Pedro J. Torres
Pedro J. Torres
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain ([email protected])
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 1 , February 2007 , pp. 195 - 201
Copyright
2007 Royal Society of Edinburgh

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