no. 4

Lyapunov center theorem for some nonlinear PDE's : a simple proof
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 4, pp. 823-837. 
@article{ASNSP_2000_4_29_4_823_0,
     author = {Bambusi, Dario},
     title = {Lyapunov center theorem for some nonlinear PDE's : a simple proof},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {823--837},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {4},
     year = {2000},
     zbl = {1008.35003},
     mrnumber = {1822409},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_4_823_0/}
}
Bambusi, Dario. Lyapunov center theorem for some nonlinear PDE's : a simple proof. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 4, pp. 823-837. http://www.numdam.org/item/ASNSP_2000_4_29_4_823_0/

[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). | MR 911772 | Zbl 0716.34083

[2] S.B. Kuksin, "Nearly Integrable Infinite-Dimensional Hamiltonian Systems", Lect. Notes Math. 1556, Springer, 1994. | MR 1290785 | Zbl 0784.58028

[3] J. Pöschel, A KAM-Theorem for some Partial Differential Equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), 119-148. | Numdam | MR 1401420 | Zbl 0870.34060

[4] W. Craig -C.E. Wayne, Newton's Method and Periodic Solutions of Nonlinear Wave Equations, Comm. Pure Appl. Math. 46 (1993), 1409-1501. | MR 1239318 | Zbl 0794.35104

[5] J. Bourgain, Construction of periodic solutions of nonlinear wave equations in higher dimension, Geom. Funct. Anal. 5 (1995), 629-639. | MR 1345016 | Zbl 0834.35083

[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 Island 1999). | MR 1662834 | Zbl 0952.35127

[7] A. Ambrosetti -G. Prodi, "A primer of Nonlinear Analysis", Cambridge University Press, Cambridge, 1993. | MR 1225101 | Zbl 0781.47046

[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] J. Mujica, "Complex Analysis in Banach Spaces.", North Holland Mathematical Studies 120, Amsterdam, 1986. | MR 842435 | Zbl 0586.46040

[10] A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer Verlag, New York, 1983. | MR 710486 | Zbl 0516.47023

[11] W.M. Schmidt, "Diophantine Approximation", Lect. Notes Math. 785, Springer, Verlag, 1980. | MR 568710 | Zbl 0421.10019

[12] J. Pöschel -E. Trubowitz, "Inversal Spectral Theory", Academic Press, Boston, 1987. | MR 894477 | Zbl 0623.34001