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.


Full Text : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA210645


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