## Abstract

We show that the generalized solutions of n-body type problems with weak forces, in R{sup l}, 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.

## Citation Formats

Riahi, H.
Study of the generalized solutions of n-body type problems with weak forces.
IAEA: N. p.,
1994.
Web.

Riahi, H.
Study of the generalized solutions of n-body type problems with weak forces.
IAEA.

Riahi, H.
1994.
"Study of the generalized solutions of n-body type problems with weak forces."
IAEA.

@misc{etde_10112406,

title = {Study of the generalized solutions of n-body type problems with weak forces}

author = {Riahi, H}

abstractNote = {We show that the generalized solutions of n-body type problems with weak forces, in R{sup l}, 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.}

place = {IAEA}

year = {1994}

month = {Oct}

}

title = {Study of the generalized solutions of n-body type problems with weak forces}

author = {Riahi, H}

abstractNote = {We show that the generalized solutions of n-body type problems with weak forces, in R{sup l}, 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.}

place = {IAEA}

year = {1994}

month = {Oct}

}