Naked singularities in dust collapse as an existence problem for O.D.E.   at a singular point
  The final state of the gravitational collapse of a marginally bound dust cloud is formulated in terms of an existence problem for the non-linear differential equation governing radial null geodesics near the singular point. Rigorous results are proved, covering the complete spectrum of the possible initial data. 
Roberto Giambo', Giulio Magli