Nontrivial periodic solutions for strong resonance hamiltonian systems

K. C. Chang; J. Q. Liu; M. J. Liu

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 1, page 103-117
  • ISSN: 0294-1449

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Chang, K. C., Liu, J. Q., and Liu, M. J.. "Nontrivial periodic solutions for strong resonance hamiltonian systems." Annales de l'I.H.P. Analyse non linéaire 14.1 (1997): 103-117. <http://eudml.org/doc/78402>.

@article{Chang1997,
author = {Chang, K. C., Liu, J. Q., Liu, M. J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {strong resonance; nonautonomous Hamiltonian system; Maslov indices; nontrivial periodic solutions},
language = {eng},
number = {1},
pages = {103-117},
publisher = {Gauthier-Villars},
title = {Nontrivial periodic solutions for strong resonance hamiltonian systems},
url = {http://eudml.org/doc/78402},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Chang, K. C.
AU - Liu, J. Q.
AU - Liu, M. J.
TI - Nontrivial periodic solutions for strong resonance hamiltonian systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 1
SP - 103
EP - 117
LA - eng
KW - strong resonance; nonautonomous Hamiltonian system; Maslov indices; nontrivial periodic solutions
UR - http://eudml.org/doc/78402
ER -

References

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  1. [AZ1] H. Amann and E. Zehnder, Nontrivial Solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Sc. Super. Pisa, CC. Sci., IV, Ser. 7, 1980, pp. 539-603. Zbl0452.47077MR600524
  2. [AZ2] H. Amann and E. Zehnder, Periodic solutions of asymptotically Hamiltonian systems, Manuscr. Math., Vol. 32, 1980, pp. 149-189. Zbl0443.70019MR592715
  3. [Ch1] K.C. Chang, Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure Appl. Math., Vol. 34, 1981, pp. 693-712. Zbl0444.58008MR622618
  4. [Ch2] K.C. Chang, Applications of homology theory to some problems in differential equations, Nonlinear Func. Anal., (F.E. BROWDER Ed.), Proc. Symp. Pure Math., AMS, 1986, pp. 253-261. Zbl0597.58003MR843564
  5. [Ch3] K.C. Chang, On the homology method in the critical point theory, PDE and related subjects, (M. MIRANDA Ed.) Pitman, Vol. 269, 1992, pp. 59-77. Zbl0798.58012MR1190934
  6. [CL] K.C. Chang and J.Q. Liu, A strong resonance problem, Chinese Ann. of Math., Vol. 11B, 1990, pp. 191-210. Zbl0719.58012MR1062090
  7. [CZ] C. Conley and E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math., Vol. 37, 1984, pp. 207-253. Zbl0559.58019MR733717
  8. [DL] Y.H. Ding and J.Q. Liu, Periodic solutions of asymptotically linear Hamiltonian systems, J. Sys. Sci. Math. Sci., Vol. 9, 1990, pp. 30-39. Zbl0659.34042MR994751
  9. [LL] S.J. Li and J.Q. Liu, Morse theory and asymptotically linear Hamiltonian systems, JDE78, 1989, pp. 53-73. Zbl0672.34037MR986153
  10. [Li] M.J. Liu, Morse theory for strong indefinite functional and applications, Thesis, Institute of System Science, Beijing, 1990. 
  11. [Lo] Y.M. Long, Maslov index, degenerate critical points and asymptotically linear Hamiltonian systems, Science in China, Ser. A, Vol. 33, 1990, pp. 1409-1419. Zbl0736.58022MR1090484
  12. [LZ] Y.M. Long and E. Zehnder, Morse theory for forced oscillations of asymptotically linear Hamiltonian systems, Stochastic Processes, Physics and Geometry, World Sci. Press, 1990, pp. 528-563. MR1124230
  13. [MP] A. Marino and G. Prodi, Metodi perturbativi nella teoria di Morse, Boll. Un. Mate. Italia, Suppl. Fasc. 3, 1975, pp. 1-32. Zbl0311.58006MR418150
  14. [Sa] A. Salvatore, Periodic solutions of asymptotically linear systems without symmetry, Rend. Sem. Mat. Univ., Padova, Vol. 74, 1985, pp. 147-161. Zbl0592.34030MR818724
  15. [Sz] A. Szulkin, Cohomology and Morse theory for strong indefinite functionals, MZ209, 1992, pp. 375-418. Zbl0735.58012MR1152264

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