For the N -centre problem in the three dimensional space,where N ≥ 2, mi > 0 and α ∈ [1, 2), we prove the existence of entire parabolic trajectories having prescribed asymptotic directions. The proof relies on a variational argument of min-max type. Morse index estimates and regularization techniques are used in order to rule out the possible occurrence of collisions.

In this paper we are concerned with a differential equation of the formwhere À14a5b4 þ 1; q has infinitely many zeros in ða; bÞ; and g is superlinear.We prove the existence of solutions with prescribed nodal properties in the intervals of negativity and positivity of q: When c ¼ 0 and q is periodic we show that the equation under consideration exhibits chaotic-like dynamics. # 2002 Elsevier Science (USA)

We prove a multiplicity result for the two-point boundary value problem associated to a second order equation of the formx, y) satisfies a sublinear condition at x = 0 and no assumption at infinity is required. We use a topological degree method based on a continuation theorem and on the performance of a time-map technique for an autonomous problem.

No abstract

Given a smooth function U (t, x), T -periodic in the first variable and satisfying U (t, x) = O(|x| α ) for some α ∈ (0, 2) as |x| → ∞, we prove that the forced Kepler problemẍhas a generalized T -periodic solution, according to the definition given in the paper [Boscaggin, Ortega, Zhao, Periodic solutions and regularization of a Kepler problem with time-dependent perturbation, Trans. Amer. Math. Soc, 2018]. The proof relies on variational arguments. Projects Dinamiche complesse per il problema degli N -centri and Proprietà qualitative di alcuni problemi ai limiti and by the project PRID SiDiA Sistemi Dinamici e Applicazioni of the DMIF -Università di Udine.