Critical point theorems for indefinite functionals

A variational principle of a minimax nature is developed and used to prove the existence of critical points for certain variational problems which are indefinite. The proofs are carried out directly in an infinite dimensional Hilbert space. Special cases of these problems previously had been tractable only by an elaborate finite dimensional approximation procedure. The main applications given here are to Hamiltonian systems of ordinary differential equations where the existence of time periodic solutions is established for several classes of Hamiltonians.Supported in part by the U.S. Army under Contract No. DAAG-29-75-C-0024 and by the Conseglio Nazionale delle Ricerche-Gruppo Nazionale Analisi Funzionale e ApplicazioneSupported in part by the J.S. Guggenheim Memorial Foundation, and by the Office of Naval Research under Contract No. N00014-76-C-0300. Reproduction in whole or in part is permitted for any purpose of the U.S. Government