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 (Formula presented.) where (Formula presented.), (Formula presented.) is a positive and positively homogeneous potential with homogeneity degree (Formula presented.) with (Formula presented.), and (Formula presented.) is a (possibly time-dependent) lower order term, for (Formula presented.), with respect to (Formula presented.). 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 (Formula presented.) -centre problem, the (Formula presented.) -body problem and the restricted (Formula presented.) -body problem) are given.