Brake subharmonic solutions of first order Hamiltonian systems

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In this paper, we mainly use 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 first order non-autonomous Hamiltonian systems. We prove that when the positive integers j and k satisfies the certain conditions, there exists a jT-periodic nonconstant brake solution zⱼ such that zⱼ and zkj are distinct.