Accession Number : ADA210645
Title : Periodic Solutions of Spatially Periodic Hamiltonian Systems
Descriptive Note : Technical summary rept.
Corporate Author : WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
Personal Author(s) : Felmer, Patricio L
Report Date : 10 Jul 1989
Pagination or Media Count : 26
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.
Descriptors : *DIFFERENTIAL EQUATIONS , *HAMILTONIAN FUNCTIONS , VARIABLES , SOLUTIONS(GENERAL) , MINIMAX TECHNIQUE , PERIODIC FUNCTIONS , HILBERT SPACE , GROWTH(GENERAL) , SIZES(DIMENSIONS)
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE