We discuss in this paper,the existence problem of periodic solutions of a nonautonomousHamiltonian system,J\dot{z}=G′_z(t,z).(*)We modify the corresponding variational functional with several factors,construct some spe-cial minimax value series and give the sharp estimates of their growth orders.Then we provethat the equation (*) possesses infinitely many periodic solutions when G(t,z)=H(z)+F(t,z) with H′_z(z) being sublinear at z=0 and with F′_z(t,z) being superlinear,and thattheir indices satisfy a certain relation.
GENG DI. , {{custom_author.name_en}}.
ON THE EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS FOR NONAUTONOMOUS HAMILTONIAN SYSTEMS. Journal of Systems Science and Mathematical Sciences, 1993, 13(4): 305-316 https://doi.org/10.12341/jssms09072