Periodic Solutions of Spatially Periodic Hamiltonian Systems
Abstract
This work is concerned with the study of existence and multiplicity of periodic solutions of Hamiltonian systems of ordinary differential equations z=J(Hz(z,t) + f(t)) when the Hamiltonian H(z,t) = H(p,q,t) is periodic in the variable q and superlinear in the variable p. By imposing a growth condition on the derivative of H, we obtain the existence of at least n + 1 periodic solutions, where n is the dimension of the system. The existence of periodic solutions is obtained by using a Saddle Point Theorem recently proved by Lui. We consider a functional over E X M, where E is a Hilbert space and M is a compact manifold, satisfying a saddle point condition on E, uniformly on M. We present a proof of this Saddle Point Theorem using standard minimax techniques based on the cup length of M.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 10, 1989
- Accession Number
- ADA210645
Entities
People
- Patricio L. Felmer
Organizations
- University of Wisconsin–Madison