Bifurcations of planar Hamiltonian systems with impulsive perturbation
  In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under which a harmonic or subharmonic solution exists. 
Zhaoping Hu, Maoan Han, Valery G. Romanovski
math.CA