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Classical Solutions for a Perturbed N-Body System

  • Gianfausto Dell’ Antonio
Conference paper
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 27)

Abstract

In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses m 1,…m N , described in cartesian coordinates
$$ x_1,...x_N,\,x_k \in R^3 \,x_k \equiv \{ x_k,1,\,x_k,2,\,x_k,3\} $$
by the system of equations
$$ m_k \ddot x_k = g\,\sum\limits_{1 \leqslant i < k \leqslant N} {\frac{{m_i m_k }}{{\left| {x_i - x_k } \right|^3 }}(x_k - x_i ) + \nabla _k w(x,t)} $$
(0.1)
where
$$ \nabla _{k,m} \equiv \frac{\partial }{{\partial x_{k.m} }},\,m = 1,2,3. $$

Keywords

Periodic Solution Weak Solution Classical Solution Critical Point Theory Kepler Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Gianfausto Dell’ Antonio
    • 1
  1. 1.Dip. di MatematicaUniv. Roma, La Sapienza Laboratorio Interdisciplinare, SISSATriesteItaly

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