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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1979
- Accession Number
- ADA079729
Entities
People
- Paul Rabinowitz
Organizations
- University of Wisconsin–Madison