New periodic solutions for the circular restricted 3-body and 4-body problems

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January 2010, 9(1): 249-260. doi: 10.3934/cpaa.2010.9.249

New periodic solutions for the circular restricted 3-body and 4-body problems

1.	College of Chengxian, Dongnan University, Nanjing 210088, China
2.	College of Mathematics, Sichuan University, Chengdu 610064, China

Received July 2008 Revised June 2009 Published October 2009

Abstract
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For the circular restricted 3-body and 4-Body problems in $\mathbb{R}^2$, we prove the existence of new symmetric noncollision periodic solutions with some fixed winding numbers and masses.

Keywords: Circular restricted 3(or 4)-body problem, noncollision periodic solutions, variational methods..

Mathematics Subject Classification: Primary: 70G75, 70F07, 70F10; Secondary: 70F1.

Citation: Qunyao Yin, Shiqing Zhang. New periodic solutions for the circular restricted 3-body and 4-body problems. Communications on Pure & Applied Analysis, 2010, 9 (1) : 249-260. doi: 10.3934/cpaa.2010.9.249

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