Scattering Parabolic Solutions for the Spatial N-Centre Problem

作者：Boscaggin Alberto^*; Dambrosio Walter; Terracini Susanna

来源：Archive for Rational Mechanics and Analysis, 2017, 223(3): 1269-1306.

DOI：10.1007/s00205-016-1057-0

For the N-centre problem in the three dimensional space,
x = Sigma(N)(i=1) m(i) (x - c(i)) vertical bar x - c(i)vertical bar(alpha+2), x is an element of R-3\{c(1), ..., c(N)},
where , and , 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.

• 出版日期2017-3