On Subharmonic Solutions of Hamiltonian Systems.

Abstract

Some existence results for T periodic solutions of (0.1) were presented in (1) for superquadratic Hamiltonian systems using finite dimensional minimax arguments together with estimates suitable to pass to a limit. An improved existence mechanism was introduced in (2) and applied to some of the super-quadratic problems of (1) as well as to several subquadratic cases. It will show here that these problems possess not only one T periodic solutions z sub 1 but infinitely many distinct subharmonic solutions z sub k. A word of caution must be entered at this point. Although z sub k has period kT, it may not be the case that z sub k has minimal (i.e. primitive) period kT. Indeed simple examples show that there may be an upper bound on the minimal period of z sub k.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1979
Accession Number
ADA079729

Entities

People

  • Paul Rabinowitz

Organizations

  • University of Wisconsin–Madison

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Communities of Interest

  • Energy and Power Technologies

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  • Analogs
  • Calculus
  • Calculus Of Variations
  • Contracts
  • Differential Equations
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Mathematics
  • Military Research
  • Periodic Functions
  • Point Theorem
  • Potential Energy
  • United States
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  • Variational Methods
  • Wisconsin

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  • Mathematics

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  • Calculus or Mathematical Analysis
  • Systems Analysis and Design