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Bibliography
AUBIN-EKELAND, "Second-order evolution equations with convex Hamiltonian", Canadian Math. Bull. 23 (1980) p. 81–94.
AUCHMUTY, "Duality for non-convex variational principles", preprint, Indiana University, Bloomington, 1981.
BREZIS-CORON-NIRENBERG, "Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz", Comm. Pure App. Math. 33 (1980), p.667–684.
CLARKE, "Solution périodique des équations hamiltoniennes", CRAS Paris, 287, 1978, p.951–2.
CLARKE, "Periodic solutions to Hamiltonian inclusions", J. Diff. Eq. 40, 1981, p.1–6.
CLARKE, "On Hamiltonian flows and symplectic transformations", SIAM J. Control and Optimization, in press.
CLARKE-EKELAND, "Solutions periodiques, de periode donnée, des équations hamiltoniennes", CRAS Paris 287, 1978, p.1013–1015.
CLARKE-EKELAND, "Hamiltonian trajectories having prescribed minimal period", Comm. Pure App. Math., 33 (1980), p.103–116.
CLARKE-EKELAND, "Nonlinear oscillations and boundary-value problems for Hamiltonian systems", Archive Rat. Mech. An., in press.
EKELAND, "Duality in non-convex optimization and calculus of variations", SIAM J. Opt. Con. 15, 1977, p.905–934.
EKELAND, "Periodic solutions to Hamiltonian equations and a theorem of P. Rabinowitz", J. Diff. Eq. 34, 1979, p.523–534.
EKELAND, "Forced oscillations for nonlinear Hamiltonian systems II", Advances in Mathematics, volume in honor of Laurent Schwartz, Nachbin ed., 1981, Academic Press.
EKELAND, "Oscillations forcées de systémes hamiltoniens non linéaires III", Bulletin de la SMF, in press.
EKELAND, "Dualité et stabili té des systémes hamiltoniens", preprint 1981.
EKELAND, "A perturbation theory near convex Hamiltonian systems", preprint, 1981.
EKELAND-LASRY, "Principes variationnels en dualité", CRAS Paris, 291 (1980), p.493–497.
EKELAND-LASRY, "Duality in nonconvex variational problems", preprint, CEREMADE, 1980.
EKELAND-LASRY, "On the number of closed trajectories for a Hamiltonian system on a convex energy surface", Annals of Math., 112 (1980), p.283–319.
EKELAND-TEMAM, "Convex analysis and variational problems", North-Holland-Elsevier, 1976.
TOLAND, "Stability of heavy rotating chains", J. Diff. Eq. 32 (1979), p.15–31.
TOLAND, "A duality principle for non-convex optimization and the calculus of variations", Arch. Rat. Mech. An. 71 (1979), p. 41–61.
TOLAND, "Duality in nonconvex optimization", J. Math. An. Appl. 66 (1978), p.41–61.
TRUC, Thése 3eme cycle, en cours, Université Paris-Dauphine.
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Ekeland, I. (1983). Dual variational methods in non-convex optimization and differential equations. In: Cecconi, J.P., Zolezzi, T. (eds) Mathematical Theories of Optimization. Lecture Notes in Mathematics, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066251
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DOI: https://doi.org/10.1007/BFb0066251
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