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Volumn 54, Issue 6, 2001, Pages 689-760

Morse homology on Hilbert spaces

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EID: 0035616758     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.1012     Document Type: Article
Times cited : (45)

References (39)
  • 1
    • 0000222362 scopus 로고    scopus 로고
    • A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces
    • Abbondandolo, A. A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces. Topol. Methods Nonlinear Anal. 9 (1997), no. 2, 325-382.
    • (1997) Topol. Methods Nonlinear Anal. , vol.9 , Issue.2 , pp. 325-382
    • Abbondandolo, A.1
  • 2
    • 0034148969 scopus 로고    scopus 로고
    • Morse theory for asymptotically linear Hamiltonian systems
    • Abbondandolo, A. Morse theory for asymptotically linear Hamiltonian systems. Nonlinear Anal. 39 (2000), no. 8, 997-1049.
    • (2000) Nonlinear Anal. , vol.39 , Issue.8 , pp. 997-1049
    • Abbondandolo, A.1
  • 4
    • 0013233280 scopus 로고    scopus 로고
    • Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order hamiltonian systems
    • Abbondandolo, A.; Molina, J. Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems. Calc. Var. 11 (2000), 395-430.
    • (2000) Calc. Var. , vol.11 , pp. 395-430
    • Abbondandolo, A.1    Molina, J.2
  • 5
    • 0001727302 scopus 로고
    • Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations
    • Amann, H.; Zehnder, E. Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 4, 539-603.
    • (1980) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.7 , Issue.4 , pp. 539-603
    • Amann, H.1    Zehnder, E.2
  • 6
    • 0004235774 scopus 로고
    • A primer of nonlinear analysis. Corrected reprint of the 1993 original
    • Cambridge University Press, Cambridge
    • Ambrosetti, A.; Prodi, G. A primer of nonlinear analysis. Corrected reprint of the 1993 original. Cambridge Studies in Advanced Mathematics, 34. Cambridge University Press, Cambridge, 1995.
    • (1995) Cambridge Studies in Advanced Mathematics , vol.34
    • Ambrosetti, A.1    Prodi, G.2
  • 7
    • 0033465124 scopus 로고    scopus 로고
    • A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology
    • Angenent, S.; van der Vorst, R. A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology. Math. Z. 231 (1999), no. 2, 203-248.
    • (1999) Math. Z. , vol.231 , Issue.2 , pp. 203-248
    • Angenent, S.1    Van Der Vorst, R.2
  • 8
    • 0003246964 scopus 로고
    • Critical points at infinity in some variational problems
    • Longman Scientific, Harlow; Wiley, New York
    • Bahri, A. Critical points at infinity in some variational problems. Pitman Research Notes in Mathematics Series, 182. Longman Scientific, Harlow; Wiley, New York, 1989.
    • (1989) Pitman Research Notes in Mathematics Series , vol.182
    • Bahri, A.1
  • 9
    • 84966212755 scopus 로고
    • Lectures on morse theory, old and new
    • Bott, R. Lectures on Morse theory, old and new. Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 331-358.
    • (1982) Bull. Amer. Math. Soc. (N.S.) , vol.7 , Issue.2 , pp. 331-358
    • Bott, R.1
  • 12
    • 84990569659 scopus 로고
    • Morse-type index theory for flows and periodic solutions for Hamiltonian equations
    • Conley, C.; Zehnder, E. Morse-type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure Appl. Math. 37 (1984), no. 2, 207-253.
    • (1984) Comm. Pure Appl. Math. , vol.37 , Issue.2 , pp. 207-253
    • Conley, C.1    Zehnder, E.2
  • 15
    • 0001827455 scopus 로고
    • Degree theory on banach manifolds
    • Nonlinear Functional Analysis Chicago, Ill., American Mathematical Society, Providence, R.I.
    • Elworthy, K.D.; Tromba, A. Degree theory on Banach manifolds. Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968), 86-94. American Mathematical Society, Providence, R.I., 1970.
    • (1968) Proc. Sympos. Pure Math. , vol.18 , Issue.PART 1 , pp. 86-94
    • Elworthy, K.D.1    Tromba, A.2
  • 16
    • 84990602558 scopus 로고
    • A relative Morse index for the symplectic action
    • Floer, A. A relative Morse index for the symplectic action. Comm. Pure Appl. Math. 41 (1988), no. 4, 393-407.
    • (1988) Comm. Pure Appl. Math. , vol.41 , Issue.4 , pp. 393-407
    • Floer, A.1
  • 17
    • 84990602491 scopus 로고
    • The unregularized gradient flow of the symplectic action
    • Floer, A. The unregularized gradient flow of the symplectic action. Comm. Pure Appl. Math. 41 (1988), no. 6, 775-813.
    • (1988) Comm. Pure Appl. Math. , vol.41 , Issue.6 , pp. 775-813
    • Floer, A.1
  • 18
    • 84972526368 scopus 로고
    • Witten's complex and infinite-dimensional Morse theory
    • Floer, A. Witten's complex and infinite-dimensional Morse theory. J. Differential Geom. 30 (1989), no. 1, 207-221.
    • (1989) J. Differential Geom. , vol.30 , Issue.1 , pp. 207-221
    • Floer, A.1
  • 19
    • 0000107242 scopus 로고    scopus 로고
    • The Conley index in Hilbert spaces and its applications
    • Gȩba, K.; Izydorek, M.; Pruszko, A. The Conley index in Hilbert spaces and its applications. Studia Math. 134 (1999), no. 3, 217-233.
    • (1999) Studia Math. , vol.134 , Issue.3 , pp. 217-233
    • Gȩba, K.1    Izydorek, M.2    Pruszko, A.3
  • 20
    • 0003284898 scopus 로고
    • The analysis of linear partial differential operators. I. Distribution theory and fourier analysis
    • Springer, Berlin-New York
    • Hörmander, L. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. Grundlehren der Mathematischen Wissenschaften, 256. Springer, Berlin-New York, 1983.
    • (1983) Grundlehren der Mathematischen Wissenschaften , vol.256
    • Hörmander, L.1
  • 22
    • 0038911650 scopus 로고    scopus 로고
    • A cohomological Conley index in Hilbert spaces and applications to strongly indefinite problems
    • in press
    • Izydorek, M. A cohomological Conley index in Hilbert spaces and applications to strongly indefinite problems. J. Differential Equations, in press.
    • J. Differential Equations
    • Izydorek, M.1
  • 23
    • 0039504313 scopus 로고    scopus 로고
    • Morse homology and degenerate Morse inequalities
    • Jiang, M. Y. Morse homology and degenerate Morse inequalities. Top. Methods Nonlinear Anal. 13 (1999), no. 1, 147-161.
    • (1999) Top. Methods Nonlinear Anal. , vol.13 , Issue.1 , pp. 147-161
    • Jiang, M.Y.1
  • 25
    • 21744451109 scopus 로고    scopus 로고
    • An infinite-dimensional Morse theory with applications
    • Kryszewski, W.; Szulkin, A. An infinite-dimensional Morse theory with applications. Trans. Amer. Math. Soc. 349 (1997), no. 8, 3181-3234.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , Issue.8 , pp. 3181-3234
    • Kryszewski, W.1    Szulkin, A.2
  • 26
    • 51249173208 scopus 로고
    • A remark on regularization in Hilbert spaces
    • Lasry, J.-M.; Lions, P.-L. A remark on regularization in Hilbert spaces. Israel J. Math. 55 (1986), no. 3, 257-266.
    • (1986) Israel J. Math. , vol.55 , Issue.3 , pp. 257-266
    • Lasry, J.-M.1    Lions, P.-L.2
  • 27
    • 84968488113 scopus 로고
    • Elliptic methods in symplectic geometry
    • McDuff, D. Elliptic methods in symplectic geometry. Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 311-358.
    • (1990) Bull. Amer. Math. Soc. (N.S.) , vol.23 , Issue.2 , pp. 311-358
    • McDuff, D.1
  • 28
    • 0001320751 scopus 로고
    • The polynomial approximation of functions on Hilbert space
    • Nemirovskiǐ, A. S.; Semenov, S. M. The polynomial approximation of functions on Hilbert space. Mat. Sb. (N.S.) 92(134) (1973), 257-281.
    • (1973) Mat. Sb. (N.S.) 92 , vol.134 , pp. 257-281
    • Nemirovskiǐ, A.S.1    Semenov, S.M.2
  • 29
    • 0001386011 scopus 로고
    • Morse theory on Hilbert manifolds
    • Palais, R. S. Morse theory on Hilbert manifolds. Topology 2 (1963), 299-340.
    • (1963) Topology , vol.2 , pp. 299-340
    • Palais, R.S.1
  • 30
    • 84990617874 scopus 로고
    • Morse theory for periodic solutions of Hamiltonian systems and the Maslov index
    • Salamon, D.; Zehnder, E. Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm. Pure Appl. Math. 45 (1992), no. 10, 1303-1360.
    • (1992) Comm. Pure Appl. Math. , vol.45 , Issue.10 , pp. 1303-1360
    • Salamon, D.1    Zehnder, E.2
  • 31
    • 0003286968 scopus 로고
    • Morse homology
    • Birkhäuser, Basel
    • Schwarz, M. Morse homology. Progress in Mathematics, 111. Birkhäuser, Basel, 1993.
    • (1993) Progress in Mathematics , vol.111
    • Schwarz, M.1
  • 33
    • 0000725045 scopus 로고
    • On gradient dynamical systems
    • Smale, S. On gradient dynamical systems. Ann. of Math. (2) 74 (1961), 199-206.
    • (1961) Ann. of Math. (2) , vol.74 , pp. 199-206
    • Smale, S.1
  • 34
    • 0001146482 scopus 로고
    • An infinite dimensional version of Sard's theorem
    • Smale, S. An infinite dimensional version of Sard's theorem. Amer. J. Math. 87 (1965), 861-866.
    • (1965) Amer. J. Math. , vol.87 , pp. 861-866
    • Smale, S.1
  • 35
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • Smale, S. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747-817.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 36
    • 51249168106 scopus 로고
    • Cohomology and morse theory for strongly indefinite functionals
    • Szulkin, A. Cohomology and Morse theory for strongly indefinite functionals. Math. Z. 209 (1992), no. 3, 375-418.
    • (1992) Math. Z. , vol.209 , Issue.3 , pp. 375-418
    • Szulkin, A.1
  • 37
    • 84972491713 scopus 로고
    • Self-dual Yang-Mills connections on non-self-dual 4-manifolds
    • Taubes, C. H. Self-dual Yang-Mills connections on non-self-dual 4-manifolds. J. Differential Geom. 17 (1982), no. 1, 139-170.
    • (1982) J. Differential Geom. , vol.17 , Issue.1 , pp. 139-170
    • Taubes, C.H.1
  • 38
    • 0000912642 scopus 로고
    • Sur une partition en cellules associée à une fonction sur une variété
    • Thom, R. Sur une partition en cellules associée à une fonction sur une variété. C. R. Acad. Sci. Paris 228 (1949), 973-975.
    • (1949) C. R. Acad. Sci. Paris , vol.228 , pp. 973-975
    • Thom, R.1
  • 39
    • 84972500802 scopus 로고
    • Supersymmetry and morse theory
    • Witten, E. Supersymmetry and Morse theory. J. Differential Geom. 17 (1982), no. 4, 661-692.
    • (1982) J. Differential Geom. , vol.17 , Issue.4 , pp. 661-692
    • Witten, E.1


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