Publications by Ivar Ekeland:
Critical point theory, calculus of variations,
Hamiltonian systems and symplectic topology


1.  "Topologie différentielle et théorie des jeux"Topology 13 (1974), p.375-388. [pdf]

2. (avec J.M. Lasry) "Sur le nombre de points critiques de fonctions invariantes par des groupes"Note CRAS Paris 282 (1976), p.559-562


3.
"Legendre duality in non-convex optimization and calculus of variations", SIAM J. Opt. and Control 15 (1977), p.905-934 [pdf]


4. "Discontinuités de champs hamiltoniens et existence de solutions optimales pour des problèmes de calcul des variations", Publications Mathématiques de l'IHES 47 (1977), p.5-32   [ps]

5.  (avec J.P. Aubin) "Second-order equations with convex Hamiltonian", Canadian Math. Bull. 23 (1980), p.81-94 [pdf]


6. (avec F. Clarke) "Solutions périodiques, de période donnée, des équations hamiltoniennes", Note CRAS Paris 287 (1978), p.1013-1015


7. (avec F. Clarke) "Hamiltonian trajectories having prescribed minimal period", Comm. Pure App. Math. 33 (1980), p.103-116 [pdf]


8. "Periodic solutions to Hamiltonian equations and a theorem of P. Rabinowitz", J. Diff. Eq. 34 (1979), p.523-534 [pdf]


9. (avec J.M. Lasry) "Nombre de solutions périodiques des équations de Hamilton", Note CRAS Paris 288 (1979), p.209-211


10. (avec J.M. Lasry) "On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface", Annals of Math.112 (1980), p.283-319 [pdf]


11. "Solutions périodiques des équations de Hamilton", in Nonlinear Partial Differential Equations and their Applications 1 (1980), Brézis and Lions ed., Pitnam, 1980


12. (avec F. Clarke) "Oscillations entretenues de systèmes hamiltoniens non linéaires", Note CRAS Paris 289 (1979), p.393-395


13. (avec F. Clarke) "Nonlinear oscillations and boundary-value problems for Hamiltonian systems", Arch. Rat. Mech. and An. 78 (1982), p.315-333


14. "Forced oscillations for nonlinear Hamiltonian systems II", Advances in Mathematics, volume in honour of L. Schwartz, Nachbin ed., Academic Press, 1981


15. (avec J.M. Lasry) "Principes variationnels en dualité", Note CRAS Paris 291 (1980), p.493-497


16. (avec J.M. Lasry) "Duality in non-convex variational problems", Advances in Hamiltonian Systems, Aubin, Bensoussan and Ekeland ed., (1983), Birkhaüser-Boston


17. "Oscillations de systèmes hamiltoniens non linéaires III", Bull. SMF, 109 (1981), p.297-330

18. "A perturbation theory near convex Hamiltonian systems", J. Diff. Eq. 50 (1983), p.407-440 [pdf]


19. "Dualité et stabilité des systèmes hamiltoniens", CRAS Paris 294 (1982), p.673-6876



20. "Dual variational methods in non-convex optimization and differential equations", Mathematical Theories of Optimization, Cecconi and Zolezzi ed., Springer Lecture Notes in Mathematics 979 (1983) p.108-120


21. "A Morse theory for Hamiltonian systems", Differential Equations, Knowles and Lewis ed., North-Holland (1984), p.165-172


22. "Une théorie de Morse pour les systèmes hamiltoniens convexes", Annales IHP "Analyse non linéaire" 1 (1984), p.19-78 [pdf]


23. "Hypersurfaces pincées et systèmes hamiltoniens", Note CRAS Paris 299 (1984), p.669-672


24. "An index theory for periodic solutions of convex Hamiltonian systems", Nonlinear Functional Analysis and its Applications, F. Browder editor, Proceedings of Symposia in Pure Mathematics 45 (1986), p. 395-423


25. (with H. Hofer) "Periodic solutions with prescribed period for convex autonomous Hamiltonian systems", Inventiones Math 81 (1985), p. 155-188


26. (with A. Ambrosetti and C. Coti Zelati) "Symmetry breaking in critical point theory and applications" J. Diff. Eq. 67 (1987), p.165-184


27. "Periodic solutions of convex Hamiltonian sysems: the index and its use", Nonlinear oscillations for conservative systems, Ambrosetti ed., Pitagora editrice, 1985


28. (avec L. Lassoued) "Un flot Hamiltonien a au moins deux trajectoires fermées sur toute surface d'énergie convexe et bornée", Note CRAS Paris 301 (1985), p.162-164


29. (avec L. Lassoued) "Multiplicité des trajectoires fermées d'un système Hamiltonien sur une hypersurface d'énergie convexe", Annales IHP "Analyse non linéaire" 4 (1987) p.1-29


30. (avec H. Hofer) "Subharmonics of convex non-autonomous Hamiltonian systems", Comm. Pure and Applied Math 40 (1987), p. 1-37


31. "Some variational problems arising from mathematical economics", Mathematical Economics, CIME Lectures 1986, Ambrosetti, Gori and Luchetti ed., Springer, Lecture Notes in Mathematics n°1330


32. (avec H. Hofer), "Sur les hypersurface convexes et leurs caractéristiques fermées", Note CRAS Paris, 304 (1987), p. 237-240


33. (avec H. Hofer) "Convex Hamiltonian energy surfaces and their closed trajectories", Comm Math. Physics 113 (1987) p.419-467


34. "Variational methods", p. 5041-5047, Systems and Control Encyclopedia, Madan Singh editor , Pergamon Press, 1987


35. "The calculus of variations: from minimization problems to critical point theory", Contributions to modern calculus of variations, Cesari editor, p. 91-101, Pitman Research Notes, Longman, 1987


36. "The mountain-pass theorem and some applications", Minimax results of Liusternik-Schnirelman type and applications, Séminaire de Mathématiques Supérieures, Université de Montréal, 1989


37. (with H. Hofer) "Two symplectic fixed-point theorems with applications to Hamiltonian dynamics", J. Math. Pures et App. 68 (1989), p.467-489


38 (with H. Hofer) "Capacités symplectiques", Note CRAS Paris, 307 (1988), p.37-40


39. (with H. Hofer) "Symplectic topology and Hamiltonian dynamics", Zeitschrift für Mathematik 200 (1989) p.355-378


40. (with B.M. d'Onofrio), "Hamiltonian systems with elliptic periodic orbits", Nonlinear Analysis TMA 14 (1990) p. 11-21


41. (with B.M. D'Onofrio) "Morse theory and the existence of periodic solutions of elliptic type", in Variational methods", Berestycki, Ekeland and Coron ed. , Birkhaüser, Progress in Nonlinear Differential Equations and their Applications, 1990, p. 447-454


42. (with V. Coti Zelati and Eric Séré), "Solutions doublement asymptotiques de systèmes hamiltoniens convexes", Note CRAS Paris 310 (1990) p. 631-633


43. (with V. Coti Zelati and Eric Séré), " A variational approach to homoclinic orbits in Hamiltonian systems", Mathematische Annalen (1990) p. 133-160


44. (with A. Ambrosetti), "Periodic solutions of a class of singular Hamiltonian systems", Proc. Royal Soc. Edinburgh 114 A(1990), p.1-13 (volume in honor of Jack Hale)


45. (with A. Ambrosetti), "Perturbation results for a class of singular Hamiltonian systems", Rendiconti dell'Academia dei Lincei, (8), 83 (1989), pp. 129-132


46. (with H. Hofer) "Symplectic topology and Hamiltonian dynamics II", Mathematische Zeitschrift, 203 (1990) p. 553-567


47. "Les solutions périodiques en mécanique analytique", Actes du Colloque sur la "Mécanique Analytique" de Lagrange et son héritage, Paris, 27-29 Septembre1989, fondation Hugot du Collége de France; Atti della Accademia delle Scienze di Torino 124 (1990) , supplemento, p.159-167


48 (with V. Coti Zelati and P.L. Lions) "Index estimates and critical points of functionals not satisfying Palais-Smale" , Annali della Scuola Normale Superiore di Pisa, Scienze Fisiche e Matematiche, Serie IV Vol XVII Fasc.4 (1990) p. 569-582


49.  (with S. Mathlouti) "Calcul numérique de la capacité symplectique", Progress in Variational Methods in Hamiltonian systems and elliptic equations, Wiley, Pitman Research Notes in Math., Ser 243, p. 68-91 (1992)


50. (with G.F. Dell'Antonio and B.M. D'Onofrio) "Stability from index estimates for periodic solutions of Hamiltonian systems", J. Diff. Eq, 108 (1994) p. 170-189


51. (with G.F. Dell'Antonio and B.M. D'Onofrio) "Les systèmes hamiltoniens convexes et pairs ne sont pas ergodiques en général", CRAS Paris, 315 (1992) p. 1413-1415


52.  (with G.F. Dell'Antonio and B.M. D'Onofrio) "Nonergodic properties of systems of oscillators coupled through convex even potentials", Variational methods in nonlinear analysis, p. 77-83, A. Ambrosetti and K.C. Chang ed. , Gordon and Breach, 1995


53. (with G.F. Dell'Antonio and B.M. D'Onofrio) "Periodic solutions of elliptic type for strongly nonlinear Hamiltonian systems", Floer memorial volume, Birkhauser, 1995, p. 327-335


54.  (with N. Ghoussoub and H. Tehrani) "Multiple solutions for a classical problem in the calculus of variations", J. Diff.Equ. 131 (1996), p. 229-243 [pdf]


55.  (with N. Ghoussoub) "Equivariant Liusternik-Schnirelman theory for non-even functionals", Annales de l'IHP, Analyse non linéaire 15 (1998) p 341-370 [pdf]


56.  (with N. Ghoussoub) "Selected new aspects of the calculus of variations in the large", Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, p.207-265  [pdf] 


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