메뉴 건너뛰기




Volumn 165, Issue 2, 2000, Pages 355-376

Iteration Inequalities of the Maslov-Type Index Theory with Applications

Author keywords

Hamiltonian system; Iteration inequality; Maslov type index; Prescribed minimal period solution

Indexed keywords


EID: 0012536240     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3775     Document Type: Article
Times cited : (37)

References (32)
  • 1
    • 0032210058 scopus 로고    scopus 로고
    • On the index theories for second order Hamiltonian systems
    • T. An and Y. Long, On the index theories for second order Hamiltonian systems, Nonlinear Anal. Theory Methods Appl. 34 (1998), 585-592.
    • (1998) Nonlinear Anal. Theory Methods Appl. , vol.34 , pp. 585-592
    • An, T.1    Long, Y.2
  • 2
    • 84980073426 scopus 로고
    • On the iteration of closed geodesics and the sturm intersection theory
    • R. Bott, On the iteration of closed geodesics and the sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171-206.
    • (1956) Comm. Pure Appl. Math. , vol.9 , pp. 171-206
    • Bott, R.1
  • 4
    • 84990569659 scopus 로고
    • Maslov-type index theory for flows and periodic solutions for Hamiltonian equations
    • C. Conley and E. Zehnder, Maslov-type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math. 37 (1984), 207-253.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 207-253
    • Conley, C.1    Zehnder, E.2
  • 5
    • 33646876246 scopus 로고    scopus 로고
    • The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
    • D. Dong and Y. Long, The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems, Trans. Amer. Math. Soc. 349 (1997), 2619-2661.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 2619-2661
    • Dong, D.1    Long, Y.2
  • 7
    • 0000279054 scopus 로고
    • Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems
    • I. Ekeland and H. Hofer, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Invent. Math. 81 (1985), 155-188.
    • (1985) Invent. Math. , vol.81 , pp. 155-188
    • Ekeland, I.1    Hofer, H.2
  • 8
    • 0030269355 scopus 로고    scopus 로고
    • Minimal period solutions of nonlinear Hamiltonian systems
    • G. Fei and Q. Qiu, Minimal period solutions of nonlinear Hamiltonian systems, Nonlinear Anal. T.M.A. 27 (1996), 821-839.
    • (1996) Nonlinear Anal. T.M.A. , vol.27 , pp. 821-839
    • Fei, G.1    Qiu, Q.2
  • 10
    • 0042886151 scopus 로고
    • Periodic solutions of convex Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity
    • M. Girardi and M. Matzeu, Periodic solutions of convex Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity, Ann. Mat. Pura Appl. 147 (1987), 21-72.
    • (1987) Ann. Mat. Pura Appl. , vol.147 , pp. 21-72
    • Girardi, M.1    Matzeu, M.2
  • 12
    • 0002278962 scopus 로고    scopus 로고
    • Hyperbolic characteristics on star-shaped hypersurfaces
    • C. Liu and Y. Long, Hyperbolic characteristics on star-shaped hypersurfaces, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 725-746.
    • (1999) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.16 , pp. 725-746
    • Liu, C.1    Long, Y.2
  • 13
    • 0001745414 scopus 로고    scopus 로고
    • An optimal increasing estimate of the iterated Maslov-type indices
    • C. Liu and Y. Long, An optimal increasing estimate of the iterated Maslov-type indices, Chinese Sci. Bull. 42 (1997), 2275-2277.
    • (1997) Chinese Sci. Bull. , vol.42 , pp. 2275-2277
    • Liu, C.1    Long, Y.2
  • 14
    • 0001630228 scopus 로고
    • Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
    • Y. Long, Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems, Scientia Sinica Ser. A 33 (1990), 1409-1419.
    • (1990) Scientia Sinica Ser. A , vol.33 , pp. 1409-1419
    • Long, Y.1
  • 15
    • 85012273335 scopus 로고
    • The minimal period problem of classical Hamiltonian systems with even potentials
    • Y. Long, The minimal period problem of classical Hamiltonian systems with even potentials, Ann. Inst. H. Poincaré Anal. Non Linéaire 10, No. 6 (1993), 605-626.
    • (1993) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.10 , Issue.6 , pp. 605-626
    • Long, Y.1
  • 16
    • 33646889177 scopus 로고
    • The minimal period problem of periodic solutions for autonomous superquadratic second order Hamiltonian systems
    • Y. Long, The minimal period problem of periodic solutions for autonomous superquadratic second order Hamiltonian systems, J. Differential Equations 111 (1994), 147-174.
    • (1994) J. Differential Equations , vol.111 , pp. 147-174
    • Long, Y.1
  • 17
    • 21944450086 scopus 로고    scopus 로고
    • On the minimal period for periodic solution problem of nonlinear Hamiltonian systems
    • Y. Long, On the minimal period for periodic solution problem of nonlinear Hamiltonian systems, Chinese Ann. Math. Ser. B 18 (1997), 481-484.
    • (1997) Chinese Ann. Math. Ser. B , vol.18 , pp. 481-484
    • Long, Y.1
  • 18
    • 0003166967 scopus 로고    scopus 로고
    • A Maslov-type index theory for symplectic paths
    • Y. Long, A Maslov-type index theory for symplectic paths, Topol. Methods Nonlinear Anal. 10 (1997), 47-78.
    • (1997) Topol. Methods Nonlinear Anal. , vol.10 , pp. 47-78
    • Long, Y.1
  • 19
    • 0001496478 scopus 로고    scopus 로고
    • Bott formulae of the Maslov-type index theory
    • Preprint Series, No. 1996-M-001, revised
    • Y. Long, Bott formulae of the Maslov-type index theory, Nankai Inst. of Math, Preprint Series, No. 1996-M-001, 1995, revised 1997; Pacific J. Math. 187 (1999), 113-149.
    • (1995) Nankai Inst. of Math
    • Long, Y.1
  • 20
    • 0001496478 scopus 로고    scopus 로고
    • Y. Long, Bott formulae of the Maslov-type index theory, Nankai Inst. of Math, Preprint Series, No. 1996-M-001, 1995, revised 1997; Pacific J. Math. 187 (1999), 113-149.
    • (1999) Pacific J. Math. , vol.187 , pp. 113-149
  • 23
    • 0034347313 scopus 로고    scopus 로고
    • Multiple periodic points of the Poincaré map of Lagrangian systems on tori
    • Y. Long, Multiple periodic points of the Poincaré map of Lagrangian systems on tori, Math. Z. 233 (2000), 443-470.
    • (2000) Math. Z. , vol.233 , pp. 443-470
    • Long, Y.1
  • 24
    • 0000850691 scopus 로고    scopus 로고
    • Indexing domains of instability for Hamiltonian systems
    • Y. Long and T. An, Indexing domains of instability for Hamiltonian systems, Nonlinear Differential Equations Appl. 5 (1998), 461-478.
    • (1998) Nonlinear Differential Equations Appl. , vol.5 , pp. 461-478
    • Long, Y.1    An, T.2
  • 25
    • 0002182215 scopus 로고
    • Morse theory for forced oscillations of asymptotically linear Hamiltonian systems
    • (S. Albeverio et al., Eds.), World Scientific, Singapore
    • Y. Long and E. Zehnder, Morse theory for forced oscillations of asymptotically linear Hamiltonian systems, in "Stocastics, Proceedings Physics and Geometry" (S. Albeverio et al., Eds.), pp. 528-563, World Scientific, Singapore, 1990.
    • (1990) Stocastics, Proceedings Physics and Geometry , pp. 528-563
    • Long, Y.1    Zehnder, E.2
  • 26
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 157-184
    • Rabinowitz, P.1
  • 27
    • 0001901435 scopus 로고
    • Minimax methods in critical point theory with applications to differential equations
    • P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. Math. 65 (1986).
    • (1986) CBMS Regional Conf. Ser. Math. , vol.65
    • Rabinowitz, P.H.1
  • 28
    • 84972538152 scopus 로고
    • On the average indices of closed geodesics
    • H.-B. Rademacher, On the average indices of closed geodesics, J. Differential Geom. 29 (1989), 65-83.
    • (1989) J. Differential Geom. , vol.29 , pp. 65-83
    • Rademacher, H.-B.1
  • 29
    • 0001776080 scopus 로고
    • A new obstruction to embedding Lagrangian tori
    • C. Viterbo, A new obstruction to embedding Lagrangian tori, Invent. Math. 100 (1990), 301-320.
    • (1990) Invent. Math. , vol.100 , pp. 301-320
    • Viterbo, C.1
  • 32
    • 0000155326 scopus 로고
    • The Maslov index for paths
    • J. Robbin and D. Salamon, The Maslov index for paths, Topology 32 (1993), 827-844.
    • (1993) Topology , vol.32 , pp. 827-844
    • Robbin, J.1    Salamon, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.