Abstract
We prove the existence of at least one T-periodic solution to a dynamical system of the type
(1) where the potentials V ij are T-periodic in t and singular at the origin, u i ε R k i=1, ..., n, and k≧3. We also provide estimates on the H 1 norm of this solution. The proofs are based on a variant of the Ljusternik-Schnirelman method. The results here generalize to the n-body problem some results obtained by Bahri & Rabinowitz on the 3-body problem in [6].
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Communicated by P. Rabinowitz
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Majer, P., Terracini, S. Periodic solutions to some problems of n-body type. Arch. Rational Mech. Anal. 124, 381–404 (1993). https://doi.org/10.1007/BF00375608
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DOI: https://doi.org/10.1007/BF00375608