By Antonio Ambrosetti (auth.), J. P. Aubin C.E.R.E.M.A.D.E., A. Bensoussan C.E.R.E.M.A.D.E., I. Ekeland C.E.R.E.M.A.D.E. (eds.)
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Additional info for Advances in Hamiltonian Systems
2). 4) W Jr~ o H(z) dt This functional is difficult to study because it is indefinite in a "strong" sense. To be more precise, it is necessary to give some definitions. A functional f on a Banach space is called "definite" if it is bounded from below (or from above) ; "semidefinite" if there exists a weakly continuous function ~ such that f + ~ is definite. f is called "indefinite" if it is not semidefinite. The spectrum of z + - Jz in L2(O,2~~2n) with periodic boun- dary conditions consits of infinitely many positive and negative eigenvalues.
C. , A variant of Ljiusternik Schnirelmann theory, to appear in J. Diff. Eq. H. CLARKE - I. EKELAND, Hamiltonian trajectories having prescribed minimal period, comm. Pure Appl. , 33, (1980), 103-116. [ E l l . EKELAND, Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz, J; Diff. , 34, (1979), 523-534. R. FADELL - S. H. RABINOWITZ, Borsuk-Ulam theorems for arbitrary SI actions and applications, Math. Research Center Technical Summary Report, University of Wisconsin-Madison, 1981.
BR 1 V. H. RABINOWITZ, Critical point theorems for indefinite functionals, Inv. , [ BCN 1 H. M. CORON - L. NIRENBERG, ~ (1979), 336-352. Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Preprint. C. , A variant of Ljiusternik Schnirelmann theory, to appear in J. Diff. Eq. H. CLARKE - I. EKELAND, Hamiltonian trajectories having prescribed minimal period, comm. Pure Appl. , 33, (1980), 103-116. [ E l l . EKELAND, Periodic solutions of Hamiltonian equations and a theorem of P.