Periodic solutions of perturbed superquadratic hamiltonian systems

Yiming Long

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 1, page 35-77
  • ISSN: 0391-173X

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Long, Yiming. "Periodic solutions of perturbed superquadratic hamiltonian systems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.1 (1990): 35-77. <http://eudml.org/doc/84068>.

@article{Long1990,
author = {Long, Yiming},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {minimax values; periodic solutions; perturbed Hamiltonian system},
language = {eng},
number = {1},
pages = {35-77},
publisher = {Scuola normale superiore},
title = {Periodic solutions of perturbed superquadratic hamiltonian systems},
url = {http://eudml.org/doc/84068},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Long, Yiming
TI - Periodic solutions of perturbed superquadratic hamiltonian systems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 1
SP - 35
EP - 77
LA - eng
KW - minimax values; periodic solutions; perturbed Hamiltonian system
UR - http://eudml.org/doc/84068
ER -

References

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  1. [1] A. Bahri - H. Berestycki, A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc.167 (1981), 1-32. Zbl0476.35030MR621969
  2. [2] A. Bahri - H. Berestycki, Forced vibrations of superquadratic Hamiltonian systems, Acta Math.152 (1984), 143-197. Zbl0592.70027MR741053
  3. [3] A. Bahri - H. Berestycki, Existence of forced oscillations for some nonlinear differential equations, Comm. Pure Appl. Math.37 (1984), 403-442. Zbl0588.34028MR745324
  4. [4] V. Benci, On critical points theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc.274 (1982), 533-572. Zbl0504.58014MR675067
  5. [5] V. Benci - P.H. Rabinowitz, Critical point theorems for indefinite functionals, Invent. Math.52 (1979), 241-273. Zbl0465.49006MR537061
  6. [6] H. Brézis - S. Wainger, A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Partial Differential Equations5(7), (1980), 773-789. Zbl0437.35071MR579997
  7. [7] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math.1 (1951), 353-367. Zbl0043.38105MR44116
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  9. [9] E.R. Fadell - P.H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math.45 (1978), 139-174. Zbl0403.57001MR478189
  10. [10] M.A. Krasnosel'skii - Y.B. Rutitsky, Convex Functions and Orlicz Spaces, Hindustan Publ. Co. (India) Delhi (1962). 
  11. [11] Y. Long, On the density of the range for some superquadratic operators, MRC Technical Summary Report 2859, University of Wisconsin-Madison (1985). 
  12. [12] Y. Long, Multiple solutions of perturbed superquadratic second order Hamiltonian systems, MRC Technical Summary Report 2963, University of Wisconsin-Madison (1987). Trans. Amer. Math. Soc.311 (1989), 749-780. Zbl0676.34026MR978375
  13. [13] Y. Long, Doctoral thesis, University of Wisconsin-Madison, 1987. 
  14. [14] I.P. Natanson, Theory of Functions of a Real Variable, Vol. 1. Frederick Ungar Publ. Co.New York (1964). Revised Edition. MR67952
  15. [ 15] R. Pisani - M. Tucci, Existence of infinitely many periodic solutions for a perturbed Hamiltonian system, Nonlinear Anal. T.M. & A. 8 (1984), 873-891. Zbl0553.34027MR753765
  16. [16] P.H. Rabinowitz, Variational methods for nonlinear eigenvalue problems, In Eigenvalues of Nonlinear Problems. Roma (1974). Ediz. Cremonese. MR464299
  17. [17] P.H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math.31 (1978), 157-184. Zbl0358.70014MR467823
  18. [18] P.H. Rabinowitz, Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math. Soc. 272 (1982), 753-769. Zbl0589.35004MR662065
  19. [19] P.H. Rabinowitz, Periodic solutions of large norm of Hamiltonian systems, J. Differential Equations50 (1983), 33-48. Zbl0528.58028MR717867

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