On Melnikov's persistency problem

Mathematical Research Letters

Volumn 4, Issue 4, 1997, Pages 445-458

  Bourgain, J ^a,b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031287692     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1997.v4.n4.a1     Document Type: Article

References (9)

1. [B1] J. Bourgain, Construction of quasi-periodic solutions of Hamiltonian perturbations of linear equations and applications to nonlinear PDE, Internat. Math. Res. Notices N11 (1994), 475-497.
2. [B2] -, Quasiperiodic solutions of Hamiltonian perturbations of 2D-linear Schrödinger equations, Ann. of Math (to appear).
3. [B3] -, Construction of periodic solutions of nonlinear wave equations in higher dimension, Geom. Funct. Anal. 4 (1995), 629-639.
4. [C-W1] W. Craig, C. Wayne, Newton's method and periodic solutions of nonlinear wave equations, Comm. Pure Appl. Math. 46 (1993), 1409-1501.
5. [C-W2] -, Periodic solutions of nonlinear Schrödinger equations and the Nash-Moser method, NATO Adv. Sci. Inst. Ser. B Phys., 331, Plenum, New York, 1994, pp. 103-122.
6. [E] L. H. Eliasson, Perturbations of stable invariant tori,. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), 115-147.
7. [Kuk] S. Kuksin, Nearly integrable infinite-dimensional Hamiltonian systems, Lecture Notes in Math, 1556, Springer-Verlag, Berlin, 1993.
8. [Pos1] J. Pöschel, On elliptic lower dimensional tori in Hamiltonian systems, Math. Z. 202 (1989), 559-608.
9. [Pos2] -, On Frölich-Spencer estimates on Green's function, Manuscripta Math. 70 (1990), 27-37.