Periodic Solutions of Spatially Periodic Hamiltonian Systems
Technical summary rept.
WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
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This work is concerned with the study of existence and multiplicity of periodic solutions of Hamiltonian systems of ordinary differential equations zJHzz,t ft when the Hamiltonian Hz,t Hp,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.
- Numerical Mathematics