Existence of Hyperbolic Orbits for N-body Type Problems
  In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Firstly, we get periodic solutions using suitable constraints, then by taking limit about a sequence of periodic solutions, we get the hyperbolic orbits. 
Donglun Wu, Shiqing Zhang
math-ph math.MP