Parabolic Orbits for a Class of Singular Hamiltonian Systems with a   Fixed Energy
  The existence of parabolic orbits is obtained for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of non-collision periodic solutions which are obtained by Mountain Pass Lemma. 
Donglun Wu and Shiqing Zhang
math.DS