Subharmonic solutions of Hamiltonian systems and the Maslov-type index theory

This paper deals with the subharmonic solutions of Hamiltonian systems ˙x = J∇H(t,x), t ∈ R1, x ∈ R2n. (H) Where H(t,x) = 12 Bˆ(t)x,x + Hˆ (t,x) is T -periodic in t , Bˆ(t) is a T -periodic semipositive symmetric matrix. We prove that for each positive integer k, (H) has a nonconstant kT -periodic solution xk such that xj and xpj are geometrically distinct if p satisfies the certain conditions. © 2006 Elsevier Inc. All rights reserved.