An abstract Nash–Moser theorem with parameters and applications to PDEs
Tài liệu tham khảo
Bambusi, 2007, Almost global existence for Hamiltonian semilinear Klein–Gordon equations with small Cauchy data on Zoll manifolds, Comm. Pure Appl. Math., 60, 1665, 10.1002/cpa.20181
Berti, 2007, Nonlinear Oscillations in Hamiltonian PDEs, vol. 74
Berti, 2008, Cantor families of periodic solutions of wave equations with Ck nonlinearities, NoDEA, 15, 247, 10.1007/s00030-007-7025-5
M. Berti, P. Bolle, Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions, Archive for Rational Mechanics and Analysis, published on line 21-1-2009
M. Berti, M. Procesi, Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces, preprint, 2009
Besse, 1978, Manifolds all of whose Geodesics are Closed
Bourgain, 1994, Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, Int. Math. Res. Not., 11, 475, 10.1155/S1073792894000516
Bourgain, 1995, Construction of periodic solutions of nonlinear wave equations in higher dimension, Geom. Funct. Anal., 5, 629, 10.1007/BF01902055
Bourgain, 1998, Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations, Ann. of Math., 148, 363, 10.2307/121001
Bourgain, 2005, Green's Function Estimates for Lattice Schrödinger Operators and Applications, vol. 158
Chierchia, 2000, KAM tori for 1D nonlinear wave equations with periodic boundary conditions, Comm. Math. Phys., 211, 497, 10.1007/s002200050824
Colin de Verdière, 1979, Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques, Comment. Math. Helv., 54, 508, 10.1007/BF02566290
Craig, 2000, Problèmes de petits diviseurs dans les équations aux dérivées partielles, vol. 9
Craig, 1993, Newton's method and periodic solutions of nonlinear wave equation, Comm. Pure Appl. Math., 4, 1409, 10.1002/cpa.3160461102
L.H. Eliasson, S. Kuksin, KAM for the nonlinear Schrödinger equation, Annals of Math., in press
Gentile, 2004, Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method, J. Math. Pures Appl. (9), 83, 1019, 10.1016/j.matpur.2004.01.007
Gentile, 2005, Periodic solutions for completely resonant nonlinear wave equations, Comm. Math. Phys., 256, 437, 10.1007/s00220-004-1255-8
Gentile, 2009, Periodic solutions for a class of nonlinear partial differential equations in higher dimension, Comm. Math. Phys., 289, 863, 10.1007/s00220-009-0817-1
Iooss, 2005, Standing waves on an infinitely deep perfect fluid under gravity, Arch. Ration. Mech. Anal., 177, 367, 10.1007/s00205-005-0381-6
Hamilton, 1982, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), 7, 65, 10.1090/S0273-0979-1982-15004-2
Hörmander, 1985, On the Nash Moser implicit function theorem, Ann. Acad. Sci. Fenn. Ser. A I Math., 10, 255, 10.5186/aasfm.1985.1028
Kuksin, 1987, Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum, Funktsional. Anal. i Prilozhen., 21, 22, 10.1007/BF02577134
Kuksin, 2000, Analysis of Hamiltonian PDEs, vol. 19
Moser, 1961, A new technique for the construction of solutions of nonlinear differential equations, Proc. Natl. Acad. Sci., 47, 1824, 10.1073/pnas.47.11.1824
Moser, 1966, A rapidly convergent iteration method and non-linear partial differential equations I & II, Ann. Sc. Norm. Super. Pisa (3), 20, 265
Pöschel, 1982, Integrability of Hamiltonian systems on Cantor sets, Comm. Pure Appl. Math., 35, 653, 10.1002/cpa.3160350504
Pöschel, 1996, A KAM-theorem for some nonlinear PDEs, Ann. Sc. Norm. Super. Pisa Cl. Sci., 23, 119
Salamon, 1989, KAM theory in configuration space, Comment. Math. Helv., 64, 84, 10.1007/BF02564665
Wayne, 1990, Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Comm. Math. Phys., 127, 479, 10.1007/BF02104499
Zehnder, 1975, Generalized implicit function theorems with applications to some small divisors problems I–II, Comm. Pure Appl. Math., 28, 91, 10.1002/cpa.3160280104
