17 citations · 43 across the 41 of their papers we have counts for
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On the symmetric central configurations for the planar 1+4-body problem
Chunhua Deng, Shiqing Zhang
We study the planar symmetric central configurations of the -body problem where the symmetry axis does not contain any infinitesimal masses. Under certain assumptions we find…
New Periodic Solutions for Newtonian -Body Problems with Dihedral Group Symmetry and Topological Constraints
Zhiqiang Wang, Shiqing Zhang
In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian -body problems. In our assumption, the particle…
Periodic Solutions for -Body-Type Problems
Fengying Li, Shiqing Zhang
We consider non-autonomous -body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity, and using Ljusternik-Schnirelmann theory, we…
Central Configurations Formed By Two Twisted Regular Polygons
Xiang Yu, Shiqing Zhang
In this paper, we study the necessary conditions and sufficient conditions for the central configurations formed by two twisted regular polygons (one N-regular polygon and one L-re…
Action Minimizing Solutions of The One-Dimensional -Body Problem With Equal Masses
Xiang Yu, Shiqing Zhang
When we use variational methods to study the Newtonian -body problem, the main problem is how to avoid collisions. C.Marchal got a remarkable result, that is, a path minimizing…
New Periodic Solutions for Some Planar -Body Problems with Newtonian Potentials
Pengfei Yuan, Shiqing Zhang
For some planar Newtonian -body problems, we use variational minimization methods to prove the existence of new periodic solutions satisfying that bodies chase each other…
Saari's Conjecture for Elliptical Type -Body Problem and An Application
Xiang Yu, Shiqing Zhang
By using an arithmetic fact, we will firstly prove Saari's conjecture in a particular case, which is called the Elliptical Type N-Body Problem, and then we apply it to prove that t…
Saari's Conjecture and Variational Minimal Solutions for -Body Problems
Yu Xiang, Zhang Shiqing
In this paper, we will prove Saari's conjecture in a particular case by using a arithmetic fact, and then, apply it to prove that for any given positive masses, the variational min…
Periodic Solutions for Circular Restricted 4-body Problems with Newtonian Potentials
Xiaoxiao Zhao, Shiqing Zhang
We study the existence of non-collision periodic solutions with Newtonian potentials for the following planar restricted 4-body problems: Assume that the given positive masses $m_{…
Nonplanar Periodic Solutions for Spatial Restricted 3-Body and 4-Body Problems
Xiaoxiao Zhao, Shiqing Zhang
In this paper, we study the existence of non-planar periodic solutions for the following spatial restricted 3-body and 4-body problems: for , given any masses $m_{1},...,…
Infinitely Many Periodic Solutions for Some N-Body Type Problems with Fixed Energies
Pengfei Yuan, Shiqing Zhang
In this paper, we apply the Ljusternik-Schnirelman theory with local Palais-Smale condition to study a class of N-body problems with strong force potentials and fixed energies. Und…
Existence of Hyperbolic Orbits for N-body Type Problems
Donglun Wu, Shiqing Zhang
In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Fir…
Nonplanar Periodic Solutions for Spatial Restricted N+1-Body Problems
Fengying Li, Shiqing Zhang, Xiaoxiao Zhao
We use variational minimizing methods to study spatial restricted N+1-body problems with a zero mass moving on the vertical axis of the moving plane for N equal masses. We prove th…
Hyperbolic Orbits for Restricted Three-body Problems with Fixed Energy
Donglun Wu, Shiqing Zhang
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtain…
Variational Minimizing Parabolic Orbits for the 2-Fixed Center Problems
Ying Lv, Shiqing Zhang
Using variational minimizing methods,we prove the existence of an odd symmetric parabolic orbit for the 2-fixed center problems with weak force type homogeneous potentials.
Planar Symmetric Concave Central Configurations in Four-body Problem
Chunhua Deng, Shiqing Zhang
In this paper, we consider the problem: given a symmetric concave configuration of four bodies, under what conditions is it possible to choose positive masses which make it central…
6-Body Central Configurations Formed by Two Isosceles Triangles
Furong Zhao, Shiqing Zhang
In this paper,we show the existence of a class of 6-body central configurations with two isosceles triangles; which are congruent to each other and keep some distance.We also study…
Stacked Central Configurations for Newtonian N+4-Body Problems
Furong Zhao, Shiqing Zhang
In this paper,we study spatial central configurations where N bodies are at the vertices of a regular N-gon and the other 4 bodies are symmetrically located on the straight lin…
Large Lagrangian Actions on Elliptical Solutions of 2-Body and 3-Body Problems with Fixed Energies
Ying Lv, Shiqing Zhang
Based on the works of Gordon ([4]) and Zhang-Zhou([8])) on the variational minimizing properties for Keplerian orbits and Lagrangian solutions of Newtonian 2-body and 3-body proble…
New Periodic Solutions of Singular Hamiltonian Systems with Fixed Energies
Fengying Li, Qingqing Hua, Shiqing Zhang
By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with…