Periodic solutions of Hamiltonian systems of 3-body type

A. Bahri; P.H. Rabinowitz

doi:10.1016/s0294-1449(16)30252-9

JournalsaihpcVol. 8, No. 6pp. 561–649

Periodic solutions of Hamiltonian systems of 3-body type

A. Bahri
École Nationale d’Ingénieurs de Tunis Campus Universitaire Le Belvédère, Tunis, Tunisie; Mathematics Department. Rutgers University, New Brunswick, NJ 08903, U.S.A.
P.H. Rabinowitz
Mathematics Department and Center for the Mathematical Sciences, University of Wisconsin, Madison, WI 53706, U.S.A.

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Abstract

We study the question of the existence of periodic solutions of Hamiltonian systems of the form:

\overset{q}{¨} + V_{q} (t, q) = 0 where V = 1 ≦ i \neq = j \sum 3 V_{ij} (t, q_{i} - q_{j}) (✶)

with $V (t, ξ)$ T-periodic in $t$ and singular at $ξ = 0$ . Under hypotheses on $V$ of 3-body type, we prove that the functional corresponding to (✶) has an unbounded sequence of critical points provided that the singularity of $V$ at 0 is strong enough.

Cite this article

A. Bahri, P.H. Rabinowitz, Periodic solutions of Hamiltonian systems of 3-body type. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), no. 6, pp. 561–649

DOI 10.1016/S0294-1449(16)30252-9