【中文摘要】 本文在张世清[30]工作基础上分别考虑具有牛顿势的平面圆形限制3体问题和4体问题,并在某些质量条件下证明了非碰撞的、且不是由中心构型生成的具有某种拓扑性质的对称解的存在性.这些解具有Bessi-Coti Zelati([4])中所介绍的对称性并加入了拓扑条件的限制.该证明利用了问题本身具有的变分结构,是以在给定的道路类上的“拉格朗日作用的最小化原理”为根据的.

【英文摘要】 Based on the work of Zhang[30], we study planar cicular restricted 3-body and 4-body problems for the Newtonian gravitational potentials respectively, and under some restrictions on masses, we prove the existence of collision-free, non homographic symmetric solutions with some topological conditions. These solutions have some symmetry, which is introduced in Bessi-Coti Zelati([4]), and taking account of a topological constraint. The argument exploits the variational structure of the problem, and is bas...