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A new approach to the Morse-Conley theory and some applications. (English) Zbl 0778.58011
The author attempted extending the Conley theory to nonlocally compact spaces. The main part of this paper is a modification of the author’s earlier paper [Recent advances in Hamiltonian systems, Proc. Int. Conf., L’Aquila/Italy 1986, 1-52 (1987; Zbl 0665.58007)].

58E05Abstract critical point theory
Full Text: DOI
[1] H. Amann -E. Zehnder,Nontrivial solutions for a class of non-resonance problems and applications to nonlinear differential equations, Annali Scuola Normale Superiore Pisa Cl. Sci., (4)7 (1980), pp. 539--603. · Zbl 0452.47077
[2] H. Amann -E. Zehnder,Periodic solutions of asymptotically linear Hamiltonian systems, Manuscripta Math.,32 (1980), pp. 149--189. Annali Scuola Normale Superiore Pisa Cl. Sci., (4)7 (1980), pp. 539--603. · Zbl 0443.70019 · doi:10.1007/BF01298187
[3] A. Ambrosetti -P. H. Rabinowitz,Dual variational methods in critical point theory and applications, J. Funct. Anal.,14 (1973), pp. 349--381. · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[4] A.Bahri,Critical points at infinity in the variational calculus, preprint. · Zbl 0667.49028
[5] A.Bahri - H.Berestycky,Existence of forced oscillations for some nonlinear differential equations, Comm. Pure Appl. Math.
[6] P. Bartolo -V. Benci -D. Fortunato,Abstract critical point theorems and applications to some problems with strong resonance at infinity, Nonlinear Analysis T.M.A.,7 (1983), pp. 981--1012. · Zbl 0522.58012 · doi:10.1016/0362-546X(83)90115-3
[7] V. Benci,A generalization of the Conley-index theory, Rendiconti Istituto Matematico di Trieste,18 (1986), pp. 16--39. · Zbl 0626.58012
[8] V. Benci,A new approach to the Morse-Conley theory,“Recent Advances in Hamiltonian systems{”,G. F. Dell’Antonio eB. D’Onofrio, Editors, World Scientific, Singapore (1986), pp. 1--52.
[9] V.Benci,Some Applications of the generalized Morse-Conley index, Conferenze del Seminario di Matematica dell’UniversitÀ di Bari,218 Laterza (1987). · Zbl 0656.58006
[10] V.Benci,Some Applications of the Morse-Conley theory to the Study of periodic solutions of Second order Conservative systems, “Periodic solutions of Hamiltonian systems andrelated topics{”, P. H.Rabinowitz, A.Ambrosetti, J.Ekeland, E. I.Zehnder, Editors, NATO ASI Series Kol,209 (1986), pp. 57--78.
[11] V. Benci,Normal modes of a Lagrangian system constrained in a potential well, Ann. Inst. H. Poincaré, A. N. L.1 (1984), pp. 401--412. · Zbl 0588.35007
[12] V. Benci,A geometrical index for the group S1 and some applications to the research of periodic solutions of O.D.E.’s, Comm. Pure Appl. Math.,34 (1981), pp. 393--432. · Zbl 0447.34040 · doi:10.1002/cpa.3160340402
[13] V. Benci,On critical point theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc.,274 (1982), pp. 533--572. · Zbl 0504.58014 · doi:10.1090/S0002-9947-1982-0675067-X
[14] V. Benci -D. Fortunato,Subharmonic solutions of prescribed minimal period for nonautonomous differential equations, “Recent Advances in Hamiltonian Systems{”,G. F. Dell’Antonio eB. M. D’Onofrio, Editors World Scientific, Singapore (1986).
[15] V.Benci - D.Fortunato,Un teorema di molteplicità per un’equazione ellittica non-lineare su varietà simmetriche, “Metodi asintotici e topologici in problemi differenziali nonlineari{”, L.Boccardo, A. M.Michelotti Editors.
[16] V.Benci - D.Fortunato,A remark on the number of nodal regions of the solutions of an elliptic superlinear equation, to appear in Proc. Roy. Soc. Edimburg. · Zbl 0686.35043
[17] V.Benci - F.Giannoni,Periodic bounce trajectories with a low number of bounce points, to appear in Ann. Inst. H. Poincaré, A. N. L. · Zbl 0667.34054
[18] V. Benci -P. H: Rabinowitz,Critical point theorems for indefinite functional, Invent. Math.,38 (1979), pp. 241--273. · Zbl 0465.49006 · doi:10.1007/BF01389883
[19] R. Bott,Lectures on Morse theory, old and new, Bull. Amer. Math. Soc.,7 (1982), pp 331--358. · Zbl 0505.58001 · doi:10.1090/S0273-0979-1982-15038-8
[20] R. Bott,On the iteration of closed geodesies and Sturm intersection theory, Com. P. A. M.,9 (1956), pp. 176--206. · Zbl 0074.17202
[21] G. Cerami,Un criterio di esistenza per i punti critici su varietà illimitate, Rc. Ist. Lomb. Sc. Lett.,112 (1978), pp. 332--336.
[22] K. C.Chang,Infinite dimensional Morse Theory and its applications, Les Presses de l’Université de Montréal (1985).
[23] K. C.Chang,A variant mountain pass lemma, Sci. Sinica Ser. A.,26 (1983). · Zbl 0544.35044
[24] C. C. Conley,Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math., 38, Amer. Math. Soc. Providence, RI, 1978. · Zbl 0397.34056
[25] C. C. Conley -E. Zehnder,Morse type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math.,37 (1984), pp. 207--253. · Zbl 0559.58019 · doi:10.1002/cpa.3160370204
[26] C. C. Conley -E. Zehnder,Subharmonic solutions and Morse theory, Physica124A, (1984), 649--658. · Zbl 0605.58015
[27] R. Churchill,Isolated invariant sets in compact metric spaces, J. Diff. Equations,12 (1972), pp. 330--352. · Zbl 0238.54044 · doi:10.1016/0022-0396(72)90036-8
[28] E. N.Dancer,Degenerate critical points, homotopy indices and Morse inequalities, Journal Für Mathematic, Bana 350 (1983). · Zbl 0669.58003
[29] I. Ekeland,Une théorie de Morse pour les systèmes Hamiltoniens convexes, Ann. Inst. H. Poincaré, Anal. Nonlinéaire,1 (1984), pp. 19--78. · Zbl 0537.58018
[30] I.Ekeland - H.Hofer,Convex Hamiltonian energy surfaces and their periodic trajectories. · Zbl 0641.58038
[31] D. Gromoll -W. Meyer,On differentiable functions with isolated critical points, Topology,8 (1969), pp. 361--369. · Zbl 0212.28903 · doi:10.1016/0040-9383(69)90022-6
[32] H. Hofer,A geometric description of the neighborhood of a critical point given by the Mountain Pass Theorem, J. London Math. Soc., (2),31 (1985), pp. 566--570. · Zbl 0573.58007 · doi:10.1112/jlms/s2-31.3.566
[33] H.Jacobowitz,Periodic solutions of x+f(t, x)=0 via the Poincaré-Birkhoff theorem, J. Diff. eq. 2{$\deg$} (1976), pp. 37. · Zbl 0285.34028
[34] A.Lazer - S.Solimini,Nontrivial solutions of operator equations and Morse indices of critical points of minimax type, Nonlinear Analysis TMA, to appear. · Zbl 0619.58011
[35] A. Marino -G. Prodi,Metodi perturbativi nella teoria di Morse, Boll. U.M.I. Suppl. Fasc.,3 (1975), pp. 115--132.
[36] F.Mercuri - G.Palmieri,Morse theory with low differentiability, preprint. · Zbl 0633.58014
[37] F.Pacella,Equivarinat Morse theory for flows and an or car on to the N-body problem, Trans. Am. Math. Soc. (1986). · Zbl 0633.58038
[38] R. S. Palais,Lusternik-Schnirelman theory on Banach manifolds, Topology,5 (1966), pp. 115--132. · Zbl 0143.35203 · doi:10.1016/0040-9383(66)90013-9
[39] R. S.Palais,Critical point theory and the minimax principle, “Global Analysis{”, Proc. Symp. Pure Math.15 (ed. S. S. Chern), Amer. Math. Soc. Providence, 1970, pp. 185--202.
[40] R. S. Palais,Morse theory on Hubert manifolds, Topology,2 (1963), pp. 299--340. · Zbl 0122.10702 · doi:10.1016/0040-9383(63)90013-2
[41] R. S. Palais -S. Smale,A generalized Morse theory, Bull. Amer. Math. Soc.,70 (1964), pp. 165--171. · Zbl 0119.09201 · doi:10.1090/S0002-9904-1964-11062-4
[42] P. H. Rabinowitz,Minimax methods in critical point theory with applications to differential equations, C.B.M.S. Regional Conf. Ser. in Math., n{$\deg$} 65, Amer. Math. Soc., Providence, RI, 1986. · Zbl 0609.58002
[43] P. H.Rabinowitz,On large norm periodic solutions of some differential equations,“Ergodic Theory and Dynamical Systems, 2 Editors E. Katok, Birkhauser (1982), pp. 193--210. · Zbl 0504.58018
[44] K. P. Rybakowski,On the homotopy index for infinite dimensional semiflows, Trans. Am. Math. Soc.,295 (1982), pp. 351--381. · Zbl 0468.58016 · doi:10.1090/S0002-9947-1982-0637695-7
[45] D.Salamon,Connected simple systems and the Conley index of isolated invariant sets, to appear in Trans. Am. Math. Soc. · Zbl 0573.58020
[46] S. Smale,An infinite dimensional version of Sard’s theorem, Amer. J. Math.,87 (1965), pp. 861--866. · Zbl 0143.35301 · doi:10.2307/2373250
[47] E. H.Spanier,Algebraic Topology, McGraw Hill (1966).
[48] S. Solimini,Existence of a third solution for a class of B.V.P. with jumping nonlinearities, Nonlinear Analysis T.M.A.,7 (1983), pp. 917--927. · Zbl 0522.35045 · doi:10.1016/0362-546X(83)90067-6
[49] G. Tian,On the mountain Pass Theorem, Kexue Tongbao,29 (1984), pp. 1150--1154. · Zbl 0588.58012