A rapidly convergent iteration method and non-linear partial differential equations - I
Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 20 (1966) no. 2, pp. 265-315.
partie suivante A rapidly convergent iteration method and non-linear differential equations = II 
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Moser, Jürgen. A rapidly convergent iteration method and non-linear partial differential equations - I. Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 20 (1966) no. 2, pp. 265-315. http://archive.numdam.org/item/ASNSP_1966_3_20_2_265_0/

1 J. Schauder, Das Anfangswertproblem einer quasilinearen hyperbolischen Differentialgleichung zweiter Order in beliebiger Anzahl von unabhängigen Veränderlichen. Fund. Math. 24, 1935, pp. 213-246. | JFM | Zbl

2 K.O. Friedrichs, Symmetric Hyperbolic Linear Differential Equation8. Comm. Pure Appl. Math. 7, 1954, pp. 345-392. | MR | Zbl

3 J. Nash, The Imbedding of Riemannian Manifolds, Ann. Math. 63, 1956, pp. 20-63. | MR | Zbl

4 J. Schwartz, On Nash's 'Implicit Function Theorem, Comm Pure Appl. Math, 13, 1960, pp. 509-530. | MR | Zbl

4' J. Mosfr, A New Technique for the Construction of Solutions of Nonlinear Differential Equations. Proc. Nat. Acad. Sciences, Vol. 47, No. 11, pp. 1824-1831, 1961. | MR | Zbl

4" J. Moser, On Invariant Curves of Area-Preserving Mappings of an Annulus. Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. IIa, No. 1, 1962, pp. 1-20. | MR | Zbl

5 C.L. Siegel, Iteration of Analytic Functions. Ann. of Math. 43, 1942, pp. 607-612. | MR | Zbl

5' C.L. Siegel, Über die Normalform Analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Nachr. Akad. Wiss., Göttingen, Math. Phys. Kl, IIa, 1952, pp. 21-30. | MR | Zbl

6 A.N. Kolmogorov, Doklad. Nauk, USSR 98, 1954, p. 527-530. | Zbl

7 A.N. Kolmogorov, General Theory of Dynamical Systems and Classical Mechanics. Proc. of Intl. Congress of Math., Amsterdam, 1954, (Amsterdam: Erven P. Nordhoff, 1957), Vol. 1, pp. 315-333. | Zbl

8 V.I. Arnold, «Small divisors » I, On mappings of a circle onto itself, Isvest. Akad. Nauk, ser. mat., 25, No. 1, 1961, pp. 21-86. | MR

9 V.I. Arnold, Small Divisor and Stability Problems in Classical ana Celestial Mechanics. Uspekhi Mat. Nauk USSR, Vol. 18, Ser. 6 (119), 1963, pp. 81-192. | MR

10 V.I. Arnold, Proof of A N. Kolmogorov's Theorem on the Preservation of Quasi-Periodic Motions under Small Perturbations of the Hamiltonian. Uspekhi Mat. N. USSR, Vol. 18, Ser. 5 (113), 1963, pp 13-40. | MR | Zbl

11 K.O. Friedrichs, Symmetric Positive Linear Differential Equations, Comm. Pure Appl. Math. 11, 1458, pp. 333-418. | MR | Zbl

12 N.N. Bogolioubov, and Y.A. Mitropolski, The Method of Integral Manifolds in Nonliriear Mechanics, Contrib. to Differential Equations, Vol. II, 1963, pp. 123-196. | Zbl

13 S.P. Diliberto, Perturbation Theorems for Periodic Surfaces. I, Rend. del Circ. Mat. Palermo (2), 9, 1961, pp. 265-299 II, Rend. del Circ. Mat. Palermo (2), 10, 1962, pp. 111-161. | MR | Zbl

13' S.P. Diliberto, Pertubation Theory of Invariant Surfaces I-IV. Mimeographed ONR Reports, Berkeley, 1956/57.

14 Kyner, W.T., Invariant manifolds, Rend. del Circolo Matematico Palermo, Ser. II, Vol. 9, 1961, pp. 98-110. | MR | Zbl

14' J.K. Hale, Integral Manifolds of Perturbed Differential Systems, Annals of Math., 73, 1961, pp. 496-531. | MR | Zbl

15 I. Kupka, Stabilité des varietés invariants d'un champ de vecteurs voui- les petites perturbations. Compt. Rend. Acad. Sc. Paris, 258, Group 1, 1964, pp. 4197-4200. | MR | Zbl

16 L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), pp. 116-162. | Numdam | MR | Zbl

17 Gagliardo, E., Ulteriori proprietà di alcune classi di funzioni in più variabili, Ricerche Mat., 8, 1959, pp. 24-51. | MR | Zbl

18 J.J. Kohn and L. Nirenberg, Non-coercive boundary value problems, to appear in Comm. Pure Appl. Math. (See under « elliptic regalarization »). | MR | Zbl

19 W.T. Kyner, A fixed point theorem. Contributions to the Theory on Nonlinear Oscillation, Vol. 3, Princeton University Press, Annals of Math. Studies 36, 1956, pp. 197-205. | MR | Zbl

20 W.T. Kyner, Small Periodic Perturbations of an Autonomous System of Vector Equations. Contributions to the Theory of Nonlinear Oscillations Vol. 4, Princeton, 1958. | MR

21 R. Sacker, On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations, NYU Report, IMM-NYLT 333, Oct. 1964, to be published in Comm. Pure Appl. Math.

22 C.L. Siegel, Vorlesungen über, Himmelsmechanik, Springer, 1956. | MR | Zbl

23 H. Cremer, über die Häufigkeit der Nichtzentren, Math. Ann. 115, pp. 607-611, 1942. | JFM

24 N. Levinson, Transformation of an analytic function of several variables to a canonical form. Duke Math. Journal 28, 1961, pp. 345-353. (See Theorem 2). | MR | Zbl

25 N.I. Achieser, Vorlesungen über Approximationstheorie, Akd. Verlag. Berlin 1953, translated from Russian, Chapter V. | MR | Zbl