We prove the existence of at least one T-periodic solution to a dynamical system of the type {Mathematical expression} (1) where the potentials Vij are T-periodic in t and singular at the origin, ui ε Rki=1, ..., n, and k≧3. We also provide estimates on the H1 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]. © 1993 Springer-Verlag.
Majer, P., Terracini, S. (1993). Periodic solutions to some problems of $n$-body type. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 124(4), 381-404 [10.1007/BF00375608].
Periodic solutions to some problems of $n$-body type
TERRACINI, SUSANNA
1993
Abstract
We prove the existence of at least one T-periodic solution to a dynamical system of the type {Mathematical expression} (1) where the potentials Vij are T-periodic in t and singular at the origin, ui ε Rki=1, ..., n, and k≧3. We also provide estimates on the H1 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]. © 1993 Springer-Verlag.
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