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<p>Using the saddle point theorem and the mountain pass theorem with Morse index estimate, the existence of periodic solutions for second-order Hamiltonian systems with mild superquadratic growth is proved in this paper. Meanwhile the existence result of homoclinic orbits for this kind of Hamiltonian systems is also obtained by the local convergence of a sequence of subharmonic solutions.</p>

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Periodic Orbits and Homoclinic Orbits of Second-order Hamiltonian Systems with Mild Superquadratic Growth

  • 期刊论文

  • 发表日期：

    2025年1月5日

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  • Xiaofei Zhang,
  • Chungen Liu,
  • Benxing Zhou

摘要

Using the saddle point theorem and the mountain pass theorem with Morse index estimate, the existence of periodic solutions for second-order Hamiltonian systems with mild superquadratic growth is proved in this paper. Meanwhile the existence result of homoclinic orbits for this kind of Hamiltonian systems is also obtained by the local convergence of a sequence of subharmonic solutions.