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Solutions of minimal period for a class of convex Hamiltonian systems. (English) Zbl 0466.70022

MSC:
70H05Hamilton’s equations
34C25Periodic solutions of ODE
58E15Applications of variational methods to extremal problems in several variables; Yang-Mills functionals
58E05Abstract critical point theory
References:
[1]Ambrosetti, A.: Esistenza di infinite soluzioni per problemi non lineari in assenza di paramentro. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat.52, 402-409 (1972)
[2]Ambrosetti, A.: On the existence of multiple solutions for a class of nonlinear boundary value problems. Rend. Sem. Mat. Univ. Padova49, 195-204 (1973)
[3]Ambrosetti, A.: A perturbation theorem for superlinear boundary value problems. M.R.C. Techn. Rep.41, No. 41 (1974)
[4]Ambrosetti, A., Mancini, G.: Remarks on some free boundary problems. To appear on ?Contributions to nonlinear partial differential equations?. Ed. H. Berestycki, H. Brezis, Pittman
[5]Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Functional Analysis14, 349-381 (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[6]Brezis, H., Coron, J.M., Nirenberg, L.: Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz (to appear)
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[8]Clarke, F., Ekeland, I.: Hamiltonian trajectories having prescribed minimal period. Comm. Fure Appl. Math.33, 103-116 (1980) · Zbl 0428.70029 · doi:10.1002/cpa.3160330202
[9]Clarke, F., Ekeland, I.: Nonlinear oscillations and boundary value problems for Hamiltonian systems (to appear)
[10]Coffmann, C.V.: A minimum-maximum principle for a class of nonlinear integral equation. J. Analyse Math.22, 391-419 (1969) · Zbl 0179.15601 · doi:10.1007/BF02786802
[11]Ekeland, I.: Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz. J. Differential Equations34, 523-534 (1979) · Zbl 0446.70019 · doi:10.1016/0022-0396(79)90034-2
[12]Hempel, J.A.: Superlinear variational boundary value problems and nonuniqueness. Thesis, Univ. New England, Aus., 1970
[13]Hempel, J.A.: Multiple solutions for a class of nonlinear boundary value problems. Ind. Univ. Math. J.20, 983-996 (1971) · Zbl 0225.35045 · doi:10.1512/iumj.1971.20.20094
[14]Nehari, Z.: Characteristic values associated with a class of nonlinear second-order differential equations. Acta Math.105, 141-175 (1961) · Zbl 0099.29104 · doi:10.1007/BF02559588
[15]Rabinowitz, P.H.: Variational methods for nonlinear eigenvalue problems, in Eigenvalues of nonlinear problems (C.I.M.E.). Ed. Cremonese
[16]Rabinowitz, P.H.: Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math.11, 137-184 (1978)
[17]Rabinowitz, P.H.: On subharmonic solutions of Hamiltonian systems (to appear)
[18]Rockafellar, R.: Convex analysis. Princeton: Princeton University Press 1970
[19]Amann, H., Zehnder, E.: Periodic solutionsof asymptotically linear Hamiltonian systems. Manuscripta Math.32, 149-189 (1980) · Zbl 0443.70019 · doi:10.1007/BF01298187
[20]Brezis, H., Coron, J.M.: Periodic solutions of nonlinear wave equations and Hamiltonian systems (to appear)
[21]Clarke, F.: Periodic solutions to Hamiltonian inclusions. To appear in J. Differential Equations.