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Symmetric periodic noncollision solutions forN-body-type problems

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Abstract

Using the calculus of variations in the large, especially computing the category of the symmetric configuration space of symmetricN-body-type problems, we prove the existence of infinitely many symmetric noncollision periodic solutions about the symmetric and nonautonomousN-body-type problems under the assumptions that the symmetric potentials satisfy the strong force condition of Gordon.

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References

  1. Bessi, U. and Coti Zelati, V.,Symmetries and noncollision closed orbits for planar N-body type problems, Nonlinear Analysis,16(1991), 587–598.

    Google Scholar 

  2. Coti Zelati, V.,The periodic solutions of N-body-type problems, Ann. Inst. H. Poincaré Analyse non Linéaire,7(1990), 477–492.

    Google Scholar 

  3. Ambrosetti, A. and Coti Zelati, V.,Pertubation of Hamiltonian systems with Keplerian potentials, Math. Z.,201(1989), 227–242.

    Google Scholar 

  4. Serre, J. P., Homologic singulier des espaces fibres, Ann. Math.,54(1951), 425–505.

    Google Scholar 

  5. Fadell, E. and Husseini, S.,A note on the category of free loop space, Proc. Amer. Math. Soc.,102(1989), 527–536.

    Google Scholar 

  6. Majer, P.,Ljusternik-Schnirelmann theory with local Palais-Smale conditions and singular dynamical systems, Ann. Inst. H. Poincaré Analyse non Linéaire,8(1991), 459–476.

    Google Scholar 

  7. Gordon, W. B.,Conservative dynamical system involving strong forces, Trans. Amer. Math. Soc.,204(1975), 113–135.

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Chongqing University Chongqing, 630044, People's Republic of China

    Zhang Shiqing

  2. Department of Mathematics, East China Normal University, 200062, Shanghai, People's Republic of China

    Zhou Qing

Authors
  1. Zhang Shiqing
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  2. Zhou Qing
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Additional information

The second author is partially supported by NSFC Grant 19141002 and a FEYUT of SEDC of China.

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Shiqing, Z., Qing, Z. Symmetric periodic noncollision solutions forN-body-type problems. Acta Mathematica Sinica 11, 37–43 (1995). https://doi.org/10.1007/BF02274045

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  • DOI: https://doi.org/10.1007/BF02274045

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