A N-body problem with weak force potential through Hamilton-Jacobi equation approach

This paper we consider for the N-body problem with potential 1/rα (0 < α < 1) the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. Here E is the Euclidean space where the bodies moving and is the norm induced by the inner product. The energy level h > 0 of the motion can also be chosen arbitrarily. We use the global viscosity solutions for the Hamilton-Jacobi equation H (x, dxu) = h and geodesics.

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