The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = J▽H(t, z(t)), where H(t, z) =1/2(B(t)z, z) +H(t, z),B(t) is a semipositive symmetric continuous matrix andH is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a_j T-periodic nonconstant brake solution z_j such that z_j and z_(kj) are distinct.
