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<p>We explore the existence of multiple periodic solutions for coupled Hamiltonian systems with distinct structural behaviors. One system exhibits the Poincaré–Birkhoff twist-type structure, while the other is characterized by a singular nonlinearity near the origin. Our results are established through a detailed phase plane analysis.</p>

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An Extension of the Poincaré–Birkhoff Theorem to Systems Having Singular Nonlinearities

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Natnael Gezahegn Mamo,
  • Andrea Sfecci,
  • Wahid Ullah

摘要

We explore the existence of multiple periodic solutions for coupled Hamiltonian systems with distinct structural behaviors. One system exhibits the Poincaré–Birkhoff twist-type structure, while the other is characterized by a singular nonlinearity near the origin. Our results are established through a detailed phase plane analysis.