Study of the generalized solutions of n-body type problems with weak forces

We show that the generalized solutions of n-body type problems with weak forces, in Rl, obtained as limits of classical solutions of problems with strong force potentials, have at most a finite number of collisions if l ≥ 2(n-2) + 1. We also estimate the number of collisions using the Morse index of the approximated solutions when l ≥ 2(n - 1) + 1 and in particular, we show the existence of a non-collision solution in the case of a symmetrical potential and l ≥ 2(n - 1) + 1. (author). 13 refs