Yuan, Pengfei; Zhang, Shiqing New periodic solutions for \(N\)-body problems with weak force potentials. (English) Zbl 1348.70028 Boll. Unione Mat. Ital. (9) 5, No. 1, 93-112 (2012). 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 Citations:Zbl 0273.49063; Zbl 0757.70007; Zbl 0771.70010; Zbl 0436.58006 PDFBibTeX XMLCite \textit{P. Yuan} and \textit{S. Zhang}, Boll. Unione Mat. Ital. (9) 5, No. 1, 93--112 (2012; Zbl 1348.70028)