Parabolic orbits in Celestial Mechanics: a functional-analytic approach

We prove the existence of half-entire parabolic solutions, asymptotic to a prescribed central configuration, for the equation x''= ∇U(x) + ∇W(t, x), x ∈ R^d, where d ≥ 2, U is a positive and positively homogeneous potential with homogeneity degree -α with α ∈ ]0,2[, and W is a (possibly time-dependent) lower order term, for vertical |x|--> +infinity, with respect to U. The proof relies on a perturbative argument, after an appropriate formulation of the problem in a suitable functional space. Applications to several problems of Celestial Mechanics (including the N-centre problem, the N-body problem and the restricted (N+H)-body problem) are given.