Brake subharmonic solutions of subquadratic Hamiltonian systems

Abstract

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 ż(t) = J∇H(t, z(t)), where $H(t,z) = \tfrac{1}{2}(\hat B(t)z,z) + \hat H(t,z),\hat B(t)$, is a semipositive symmetric continuous matrix and Ĥ 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.

Keywords

Brake subharmonic solution / L-Maslov type index / Hamiltonian systems

References

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