A Variational Approach to Heteroclinic Orbits for a Class of Hamiltonian Systems
Abstract
A large literature has developed in the last decade in which methods from the calculus of variations have been used to prove the periodic solutions of Hamiltonian systems of ordinary differential equations. The recent monograph of Mawhin and Willem provides a sizable bibliography of such works. Aside from equilibria, periodic solutions are the simplest global in time solutions of differential equations. It is only within the past one - two years that attempts have begun to extend the variational approach to such systems to find other kinds of global solutions of Hamiltonian systems. Thus far mainly homoclinic orbits have been treated. However heteroclinic orbits were studied in an earlier work by the author, entitled Periodic and Heteroclinic orbits for a Periodic Hamiltonian system, for the class of second order Hamiltonian systems. The author's goal in this paper is to extend one of the main results in his earlier work mentioned above.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1990
- Accession Number
- ADA219853
Entities
People
- Paul Rabinowitz
Organizations
- University of Wisconsin–Madison