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Minimal period estimates on P-symmetric periodic solutions of first-order mild superquadratic Hamiltonian systems


With the aid of P-index iteration theory, we consider the minimal period estimates on P-symmetric periodic solutions of nonlinear P-symmetric Hamiltonian systems with mild superquadratic growth.

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The first author was supported by the Youth Fund Programs of the Science and Technology Department in Shanxi (Grant No. 201901D211430), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2019L0766), and the Doctoral Scientific Research Foundation of Shanxi Datong University. The second author was partially supported by the National Natural Science Foundation of China (Grant No. 11790271), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020A1515011019), and the Innovation and Development Project of Guangzhou University.

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Correspondence to Chungen Liu.

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Zhang, X., Liu, C. Minimal period estimates on P-symmetric periodic solutions of first-order mild superquadratic Hamiltonian systems. Front. Math. China 16, 239–253 (2021).

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  • Hamiltonian system
  • P-symmetric periodic solution
  • P-index
  • minimal period


  • 34B05
  • 37B30
  • 58E05
  • 70H05