Journal of Lanzhou University of Technology ›› 2024, Vol. 50 ›› Issue (2): 169-172.

• Scientific • Previous Articles    

The multiplicity of periodic solutions for Hamiltonian systems with a local superquadratic condition

WANG Ming-wei1, FENG Xin-xin2, ZHU Ya-pei2   

  1. Foundational Courses Department, Agricultural University of Hebei, Cangzhou 061100, China
  • Received:2022-10-13 Online:2024-04-28 Published:2024-04-29

Abstract: The multiplicity of periodic solutions for a class of second-order Hamiltonian systems with local superquadratic conditions is studied via the Symmetric Mountain Pass Lemma. Infinitely many critical points of the energy functional of the system are obtained. Under this local superquadratic condition, it is demonstrated that the second-order Hamiltonian system has infinitely many periodic solutions.

Key words: second-order Hamiltonian systems, periodic solutions, multiplicity, local super-quadratic

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