摘要
Let P C Sp（2n） satisfying pk = I2n. We consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system x（t） = JH＇（x（t））. For some symplectic matrices P, we show that for any π 〉0,the above Hamiltonian system possesses a kT periodic solution x with kT being its minimal P-symmetric period provided H satisfies Rabinowitz＇s conditions on the minimal period conjecture, together with that H is convex and H（Px） = H（x）.
Let P C Sp（2n） satisfying pk = I2n. We consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system x（t） = JH＇（x（t））. For some symplectic matrices P, we show that for any π 〉0,the above Hamiltonian system possesses a kT periodic solution x with kT being its minimal P-symmetric period provided H satisfies Rabinowitz＇s conditions on the minimal period conjecture, together with that H is convex and H（Px） = H（x）.
基金
This work was partially supported by the National Natural Science Foundation of China （Grant No. 11471170）.
