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.)

ISBN-10: 0817631305

ISBN-13: 9780817631307

ISBN-10: 146846728X

ISBN-13: 9781468467284

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Let A ER+ be given. If u E E is a criti- cal point of (1. 9) then \ z -t (u) 27T J27T J 0 __ + 0 G(u) u E E = VG(u) is a 2n-periodic solution of (H)A. 3 : Here SE ~ + ~) ER 2N it results = Az • (1,2). 9» is bounded from below. 3», implies m m o um has minimal period 27T : period T = 27TA • VG(u(~)) is a solution of (H) with minimal We now consider, following [17 I, the superquadratic case, namely S >2 • In this case J A is unbounded from below (as well as from above) but J: 7T G(u) is dominating near u =0 and so J A has a strict local minimum at zero. __

An"a!. ~ [ BI ] v. BENe I , , (1973), 349-381. A geometrical Index for the group SI and some applications to the study of periodic solutions of ordinary differential equations, comm. Pure Appl. , 34 (1981), 393-432. [B2 ] v. BENCI, On the critical point theory for indefinite func- tionals in the presence of symmetries, to appear in Trans. Amer. Math. Soc. [ BCFI ] V. BENCI - A. CAPOZZI - D. FORTUNADO, Periodic solutions of Hamiltonian systems with a prescribed period, Preprint. [ BCF2 ] V. BENCI - A.

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. R. H. RABINOWITZ, Generalized cohomological index theories for Lie "group actions with an application to bifurcation questions for Hamiltonian systems, Inv. , 45, (1978), 139-174.

### Advances in Hamiltonian Systems 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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