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Open Access Research

Periodic solutions for N + 2 -body problems with N + 1 fixed centers

Furong Zhao12*, Fengying Li2 and Jian Chen23

Author Affiliations

1 Department of Mathematics and Computer Science, Mianyang Normal University, Mianyang, Sichuan, 621000, P.R. China

2 Department of Mathematics, Sichuan University, Chengdu, 610064, P.R. China

3 School of Science, Southwest University of Science and Technology, Mianyang, Sichuan, 621000, P.R. China

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Boundary Value Problems 2013, 2013:129  doi:10.1186/1687-2770-2013-129

Published: 17 May 2013

Abstract

In this paper, we prove the existence of a new periodic solution for <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M1">View MathML</a>-body problems with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M2">View MathML</a> fixed centers and strong-force potentials. In this model, N particles with equal masses are fixed at the vertices of a regular N-gon and the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M5">View MathML</a>th particle is fixed at the center of the N-gon, the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M6">View MathML</a>th particle winding around N particles.

MSC: 34C15, 34C25, 70F10.

Keywords:
<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M1">View MathML</a>-body problems with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/129/mathml/M2">View MathML</a>-fixed centers; minimizing variational methods; strong-force potentials