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New periodic solutions for \(N\)-body problems with weak force potentials. (English) Zbl 1348.70028

Summary: In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz [J. Funct. Anal. 14, 349–381 (1973; Zbl 0273.49063)] and Ambrosetti-Coti Zelati [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 9, 187–200 (1992; Zbl 0757.70007), addendum 9, No. 3, 337–338 (1992; Zbl 0771.70010)] with \((CPS)_c\) type condition of Cerami-Palais-Smale [G. Cerami, Rend., Sci. Mat. Fis. Chim. Geol. 112, 332–336 (1978; Zbl 0436.58006)] to study the existence of new periodic solutions with a prescribed energy for \(N\)-body problems with weak force type potentials.

MSC:

70F10 \(n\)-body problems
34C25 Periodic solutions to ordinary differential equations
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
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