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

  • Pedro J. Torres (a1)
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.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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