Nonplanar periodic solutions for spatial restricted 3-body and 4-body problems

@article{Zhao2012NonplanarPS,
  title={Nonplanar periodic solutions for spatial restricted 3-body and 4-body problems},
  author={Xiaoxia Zhao and Shiqing Zhang},
  journal={Boundary Value Problems},
  year={2012},
  volume={2015},
  pages={1-10}
}
In this paper, by using variational methods, we study the existence of nonplanar periodic solutions for the following spatial restricted 3-body and 4-body problems: for N=2 or 3$N=2 \mbox{ or } 3$, N mass points with positive masses m1,…,mN$m_{1},\ldots,m_{N}$ move in a central configuration (for N=2$N=2$, two bodies are in a Euler configuration; for N=3$N=3$, three bodies are in a Lagrange configuration), and they move in the plane of N circular obits; the N+1$N+1$th mass point, called the… 
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Variational Methods, 3rd edn

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