Erratum to: "Quasi-periodic solutions of completely resonant nonlinear wave equations" [J. Differential Equations 230 (2006) 213-274] (DOI:10.1016/j.jde.2005.12.012);Quasi-periodic solutions of completely resonant nonlinear wave equations

Journal of Differential Equations

Volumn 230, Issue 1, 2006, Pages 213-274

  Yuan, Xiaoping ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Completely resonant; Invariant torus; KAM theorem; Nonlinear wave equation; Quasi periodic solution

Indexed keywords

EID: 33748285996     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.09.016     Document Type: Erratum

References (28)

1. Bambusi D., and Paleari S. Families of periodic orbits for resonant PDEs. J. Nonlinear Sci. 11 (2001) 69-87
2. Birkhoff G.D. Dynamical Systems. Amer. Math. Soc. Colloq. Publ. vol. IX (1927), Amer. Math. Soc., New York
3. Bobenko A.I., and Kuksin S. The nonlinear Klein-Gordon equation on an interval as perturbed sine-Gordon equation. Comment. Math. Helv. 70 (1995) 63-112
4. Bogoljubov N.N., Mitropolskii Yu.A., and Samoilenko A.M. Methods of Accelerated Convergence in Nonlinear Mechanics (1976), Springer, New York (Russian original: Naukova Dumka, Kiev, 1969)
5. Bourgain J. Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and application to nonlinear PDE. Int. Math. Res. Not. 11 (1994) 475-497
6. Bourgain J. Periodic solutions of nonlinear wave equations. Harmonic Analysis and Partial Equations (1999), Chicago Univ. Press, Chicago 69-97
7. Brézis H. Periodic solutions of nonlinear vibrating strings and duality principles. Bull. Amer. Math. Soc. 8 (1983) 409-426
8. Bricmont J., Kupiainen A., and Schenkel A. Renormalization group and the Melnikov problems for PDEs. Comm. Math. Phys. 221 (2001) 101-140
9. Chierchia L., and You J. KAM tori for 1D nonlinear wave equations with periodic boundary conditions. Comm. Math. Phys. 211 (2000) 497-525
10. Craig W., and Wayne C. Newton's method and periodic solutions of nonlinear wave equation. Comm. Pure Appl. Math. 46 (1993) 1409-1501
11. Dieckerhoff R., and Zehnder E. Boundedness of solutions via twist theorem. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (1987) 79-95
12. Eliasson L.H. Reducibility and point spectrum for linear quasi-periodic skew-products. Proceedings of ICM 1998, Vol. II. Doc. Math. (extra) (1998) 779-787
13. Gentile G., Mastropietro V., and Procesi M. Periodic solutions for completely resonant nonlinear wave equations. Comm. Math. Phys. 256 (2005) 437-490
14. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals, Series, and Products (1980), Academic Press, New York
15. Kuksin S.B. Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum. Funct. Anal. Appl. 21 (1987) 192-205
16. Kuksin S.B. Nearly Integrable Infinite-Dimensional Hamiltonian Systems. Lecture Notes in Math. vol. 1556 (1993), Springer, New York
17. Kuksin S.B. Elements of a qualitative theory of Hamiltonian PDEs. Proceedings of ICM 1998, Vol. II. Doc. Math. (extra) (1998) 819-829
18. Kuksin S.B., and Pöschel J. Invariant Cantor manifolds of quasiperiodic oscillations for a nonlinear Schrödinger equation. Ann. of Math. 143 (1996) 149-179
19. 3 = 0. Funct. Anal. Appl. 22 (1988) 332-333
20. Marmi S., and Yoccoz J.-C. Some Open Problems Related to Small Divisors. Lecture Notes in Math. vol. 1784 (2002), Springer, New York
21. Meyer K.R., and Hall G.R. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Appl. Math. Sci. vol. 90 (1992), Springer, New York
22. Pöschel J. A KAM-theorem for some nonlinear PDEs. Ann. Sc. Norm. Super. Pisa Cl. Sci. IV Ser. (15) 23 (1996) 119-148
23. Pöschel J. Quasi-periodic solutions for nonlinear wave equation. Comment. Math. Helv. 71 (1996) 269-296
24. Procesi M. Quasi-periodic solutions for completely resonant nonlinear wave equations in 1D and 2D. Discrete Contin. Dyn. Syst. 13 (2005) 541-552
25. Wayne C.E. Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Comm. Math. Phys. 127 (1990) 479-528
26. Yuan X. Lagrange stability for Duffing-type equations. J. Differential Equations 160 (2000) 94-117
27. Yuan X. Invariant manifold of hyperbolic-elliptic type for nonlinear wave equation. Int. J. Math. Math. Sci. 18 (2003) 1111-1136
28. X. Yuan, Quasi-periodic solutions of nonlinear wave equations with a prescribed potential, Discrete Contin. Dyn. Syst., submitted for publication