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T-periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity. (English) Zbl 0467.35009

MSC:
35B10 Periodic solutions to PDEs
35A15 Variational methods applied to PDEs
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:
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[2] AMANN, H./ZEHNDER, E.: Multiple periodic solutions of asymptotically linear Hamiltonian systems, to appear · Zbl 0443.70019
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[4] BERGER, M.S.: Nonlinearity and Functional Analysis, New York, Academic Press, 1977 · Zbl 0368.47001
[5] CLARK, D.: A variant of the Lusternik-Schnirelmantheory, Indiana Univ. Math. J., 22, 1972, 65–74 · Zbl 0228.58006 · doi:10.1512/iumj.1972.22.22008
[6] –: Periodic solutions of variational systems of ordinary differential equations, J. of Diff. Equations, 28, 1978, 354–368 · Zbl 0369.34019 · doi:10.1016/0022-0396(78)90133-X
[7] RABINOWITZ, P.H.: Some minimax theorems and applications to nonlinear partial differential equations, in: Nonlinear Analysis, A volume dedicated to E. Rothe, ed. by L. Cesari, R. Kannan, H. Weinberger, New York, Academic Press 1978 · Zbl 0466.58015
[8] –: A variational method for finding periodic solutions of differential equations, Nonlinear Evolution Equations (M.G. Crandall ed.), New York, Academic Press, 1978, 225–251
[9] THEWS, K.: Non-trivial solutions of elliptic equations at resonance, Proc. of the Royal Soc. of Edinburgh, 85A, 1980, 119–129 · Zbl 0431.35040
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