Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions : slow oscillations of beams on elastic bearings

Eduard Feireisl

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1993)

  • Volume: 20, Issue: 1, page 133-146
  • ISSN: 0391-173X

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Feireisl, Eduard. "Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions : slow oscillations of beams on elastic bearings." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 20.1 (1993): 133-146. <http://eudml.org/doc/84140>.

@article{Feireisl1993,
author = {Feireisl, Eduard},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Rayleigh-Ritz method; Hilbert spaces; transversal displacement equation; variational formulation; spectral analysis; linear operator},
language = {eng},
number = {1},
pages = {133-146},
publisher = {Scuola normale superiore},
title = {Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions : slow oscillations of beams on elastic bearings},
url = {http://eudml.org/doc/84140},
volume = {20},
year = {1993},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions : slow oscillations of beams on elastic bearings
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1993
PB - Scuola normale superiore
VL - 20
IS - 1
SP - 133
EP - 146
LA - eng
KW - Rayleigh-Ritz method; Hilbert spaces; transversal displacement equation; variational formulation; spectral analysis; linear operator
UR - http://eudml.org/doc/84140
ER -

References

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  1. [1] H. Brézis: Periodic solutions to nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc.8, 409-426 (1983). Zbl0515.35060MR693957
  2. [2] H. Brézis - J.M. Coron - L. Nirenberg: Free vibrations for a nonlinear wave equation and the theorem of P. Rabinowitz, Comm. Pure Appl. Math.33, 667-689 (1980). Zbl0484.35057MR586417
  3. [3] G. Capriz: Self-excited vibrations of rotors, International Union of Theoretical and Applied Mechanics, Sympos. Lyngby/Denmark 1974, Springer-Verlag1975. Zbl0318.73068
  4. [4] G. Capriz - A. Laratta: Large amplitude whirls of rotors, Vibrations in Rotating Machinery, Churchill College, Cambridge1976. 
  5. [5] E. Feireisl: Time periodic solutions to a semilinear beam equation, Nonlinear Anal.12, 279-290 (1988). Zbl0657.35089MR928562
  6. [6] P.H. Rabinowitz: Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math.31, 31-68 (1978). Zbl0341.35051MR470378
  7. [7] A. Salvatore: Solutions of minimal period for a semilinear wave equation, Ann. Mat. Pura Appl.155 (4), 271-284 (1989). Zbl0714.35052MR1042839
  8. [8] K. Tanaka: Forced vibrations for a superlinear vibrating string equation, Recent topics in nonlinear PDE III, Tokyo1986, Lecture Notes Numer. Appl. Anal. 9, 247-266 (1987). Zbl0651.35055MR928195
  9. [9] G. Tarantello: Solutions with prescribed minimal period for nonlinear vibrating strings, Comm. Partial Differential Equations12, 1071-1094 (1987). Zbl0628.35007MR888007
  10. [10] S. Timoshenko - D.H. Young - W. WeaverJr.: Vibrations Problems in Engineering, 4th ed., John Wiley and Sons, New York1974. 

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