Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors (Q1430332)

The author studies the existence of sub-harmonics for the following first-order Hamiltonian system \[ -J\cdot \dot u-B(t)\cdot =\nabla H(t,u),\quad u\in\mathbb R^{2N},\;t\in\mathbb R, \] where \(B(t)\) is a given continuous \(T\)-periodic and symmetric \(2N\times 2N\)-matrix function, \(H\in C^1 (\mathbb R\times \mathbb R^{2N},\mathbb R)\) is \(T\)-periodic in \(t\), and \(J\) is the standard symplectic matrix \(\left(\begin{smallmatrix} 0 &-I_N\\ I_N &0 \end{smallmatrix} \right)\).