Lyapunov center theorem for some nonlinear PDE's : a simple proof

Dario Bambusi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 4, page 823-837
  • ISSN: 0391-173X

How to cite

top

Bambusi, Dario. "Lyapunov center theorem for some nonlinear PDE's : a simple proof." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.4 (2000): 823-837. <http://eudml.org/doc/84429>.

@article{Bambusi2000,
author = {Bambusi, Dario},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {small oscillations; nonresonance; nonlinear partial differential equation},
language = {eng},
number = {4},
pages = {823-837},
publisher = {Scuola normale superiore},
title = {Lyapunov center theorem for some nonlinear PDE's : a simple proof},
url = {http://eudml.org/doc/84429},
volume = {29},
year = {2000},
}

TY - JOUR
AU - Bambusi, Dario
TI - Lyapunov center theorem for some nonlinear PDE's : a simple proof
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 4
SP - 823
EP - 837
LA - eng
KW - small oscillations; nonresonance; nonlinear partial differential equation
UR - http://eudml.org/doc/84429
ER -

References

top
  1. [1] S.B. Kuksin, Hamiltonian Perturbations of Infinite-dimensional LinearSystems with Imaginary Spectrum, Funktsional. Anal. i Prilozhen.21 (3) (1987), 22-37, Translated in Funct. Anal. Appl.21 (1987). Zbl0716.34083MR911772
  2. [2] S.B. Kuksin, "Nearly Integrable Infinite-Dimensional Hamiltonian Systems", Lect. Notes Math.1556, Springer, 1994. Zbl0784.58028MR1290785
  3. [3] J. Pöschel, A KAM-Theorem for some Partial Differential Equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), 119-148. Zbl0870.34060MR1401420
  4. [4] W. Craig — C.E. Wayne, Newton's Method and Periodic Solutions of Nonlinear Wave Equations, Comm. Pure Appl. Math.46 (1993), 1409-1501. Zbl0794.35104MR1239318
  5. [5] J. Bourgain, Construction of periodic solutions of nonlinear wave equations in higher dimension, Geom. Funct. Anal.5 (1995), 629-639. Zbl0834.35083MR1345016
  6. [6] J. Bourgain, Nonlinear Schrödinger equations, In "Hyperbolic equations and frequency interactions" ; L. Caffarelli, E. Weinan editors. IAS/Park City mathematics series 5. American Mathematical Society (Providence, Rhode Island1999). Zbl0952.35127MR1662834
  7. [7] A. Ambrosetti — G. Prodi, "A primer of Nonlinear Analysis", Cambridge University Press, Cambridge, 1993. Zbl0781.47046MR1225101
  8. [8] R. De La Llave, Variational methods for quasi-periodic solutions of partial differential equations, preprint 1999 available in mparc (http://www.ma.utexas.edu/mp_arc/), n°00-56. 
  9. [9] J. Mujica, "Complex Analysis in Banach Spaces.", North Holland Mathematical Studies120, Amsterdam, 1986. Zbl0586.46040MR842435
  10. [10] A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer Verlag, New York, 1983. Zbl0516.47023MR710486
  11. [11] W.M. Schmidt, "Diophantine Approximation", Lect. Notes Math.785, Springer, Verlag, 1980. Zbl0421.10019MR568710
  12. [12] J. Pöschel — E. Trubowitz, "Inversal Spectral Theory", Academic Press, Boston, 1987. Zbl0623.34001MR894477

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.