For the spatial generalized N -centre problemwhere mi > 0 and α ∈ [1, 2), we prove the existence of positive energy entire solutions with prescribed scattering angle. The proof relies on variational arguments, within an approximation procedure via (free-time) boundary value problems. A self-contained appendix describing a general strategy to rule out the occurrence of collisions is also included.1991 Mathematics Subject Classification. 37J45, 70F05, 70F16.
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