Abstract
This paper contains results concerning the existence of long periodic solutions of nonautonomous Hamiltonian systems near the origin.
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- ARNOLD,V.I.: Mathematical Methods of Classical Mechanics. Berlin-Heidelberg-New York; Springer-Verlag 1978
- BENCI,V.-CAPOZZI,A.-FORTUNATO,D.: Periodic solutions of Hamilt onian systems with superquadratic potential, Ann.Mat.Pura Appl.143, 1–46, (1986)
- BENCI,V. -RABINOWITZ,P.H.: Critical point theorems for indefinite functionals. Inv.Math.52, 336–352, (1979)
- BIRKHOFF,G.D.-LEWIS,D.C.: On the periodic motions near a given periodic motion of a dynamical system. Ann.Mat.Pura Appl.12, 117–133, (1933)
- GELFAND,I.-LIDSKY,V.: On the structure of regions of stability of linear canonical systems of differential equations with periodic coefficients, Uspekhi Mat.Naouk,10, (1955), 3–40 (A.M.S.Translation,8, 143–181, (1958))
- HARRIS,T.C.: Periodic solutions of arbitrarily long periods in Hamiltonian systems. J.Diff.Eq.4, 131–141, (1968)
- JÖRGENS, K. -WEIDMANN, J.: Spectral properties of Hamiltonian operators. Berlin-Heidelberg-New York; Springer-Verlag lecture notes in Math., (1973)
- KREIN,M.: Generalization of certain investigations of A.H.Liapounov on linear differential equations with periodic coefficients. Doklady Akad.Naouk, USSR,73, 445–448, (1950)
- MOSER, J.: Proof of a generalized form of a fixed point theorem due to G.D.Birkhoff. Berlin-Heidelberg-New York: Springer-Verlag lecture notes in Math.,597, 464–494, (1977)
- RABINOWITZ,P.H.: On Subharmonic solutions of Hamiltonian systems. Comm.Pure Appl.Math.,33, 609–633, (1980)
- RABINOWITZ,P.H.: Minimax Methods in Critical point Theory with applications to differential equations. Conference series in Mathematics, A.M.S.,65, (1986)
- TARANTELLO,G.: Subharmonic solutions for Hamiltonian systems via aZ p pseudoindex theory, preprint
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Benci, V., Fortunato, D. A “Birkhoff-Lewis” type result for a class of Hamiltonian systems. Manuscripta Math 59, 441–456 (1987). https://doi.org/10.1007/BF01170847
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DOI: https://doi.org/10.1007/BF01170847