Infinitely Many Periodic Solutions for Some N-Body Type Problems with Fixed Energies

TL;DR

This paper proves the existence of infinitely many symmetrical periodic solutions in certain N-body problems with fixed energies using advanced variational methods.

Contribution

It introduces a novel application of Ljusternik-Schnirelman theory to establish multiple periodic solutions for N-body problems with strong force potentials.

Findings

Existence of infinitely many non-constant periodic solutions

Solutions are symmetrical and non-collision

Applicable to N-body problems with fixed energies

Abstract

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. Under suitable conditions on the potential $V$, we prove the existence of infinitely many non-constant and non-collision symmetrical periodic solutions .