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<p>We investigate the problem of periodic bouncing solutions and unbounded solutions for a class of elastic impact oscillators of Hill’s type. By constructing an auxiliary system, we transform the study of periodic bouncing solutions into the analysis of a continuous first-order system. This new approach to impact problems, combined with the Poincaré-Birkhoff theorem, enables us to establish the existence of infinitely many periodic bouncing solutions. Furthermore, we demonstrate that large amplitude solutions become unbounded when the mean value of the weight function is negative.</p>

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Periodic Bouncing Solutions and Unbounded Solutions for a Class of Hill’s Type Impact Oscillators

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Chunlian Liu,
  • Chao Wang,
  • Zhiguo Wang

摘要

We investigate the problem of periodic bouncing solutions and unbounded solutions for a class of elastic impact oscillators of Hill’s type. By constructing an auxiliary system, we transform the study of periodic bouncing solutions into the analysis of a continuous first-order system. This new approach to impact problems, combined with the Poincaré-Birkhoff theorem, enables us to establish the existence of infinitely many periodic bouncing solutions. Furthermore, we demonstrate that large amplitude solutions become unbounded when the mean value of the weight function is negative.