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） = JVH...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） = JVH（t, z（t））, where H（t, z） = 1/2（B（t）z, z） ＋ H（t, z）, B（t） is a semipositive symmetric continuous matrix and H is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11501030,11226156)the Beijing Natural Science Foundation(No.1144012)
文摘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） = JVH（t, z（t））, where H（t, z） = 1/2（B（t）z, z） ＋ H（t, z）, B（t） is a semipositive symmetric continuous matrix and H is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.
