Periodic and subharmonic solutions for a class of the second-order Hamiltonian systems with impulsive effects (Q2342474)

The paper studies the following second-order impulsive Hamiltonian systerm \[ -q''(t)=\nabla F(t,q(t)), \quad t\not=t _j, \quad t\in \mathbb{R}, \] \[ \Delta q'(t_j)=-g_j(q(t_j)),\quad j\in \mathbb{Z}. \] The main results are obtained by variational methods and critical point theory, more specifically, by the Linking Theorem. The paper generalizes the well-known Ambrosetti-Rabinowitz condition concerning sufficient conditions for the existence of periodic and subharmonic solutions of the above problem.