Moser, Jürgen
A rapidly convergent iteration method and non-linear differential equations = II
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3 : Tome 20 (1966) no. 3 , p. 499-535
MR 206461 | 12 citations dans Numdam
⇒ partie précédente A rapidly convergent iteration method and non-linear partial differential equations - I
URL stable : http://www.numdam.org/item?id=ASNSP_1966_3_20_3_499_0

Bibliographie

1 J. Schauder, Das Anfangsvertproblem einer quasi-linearen hyperbolischen Differentialgleichung zweiter Order in beliebige), Anzahl von unabhängigen Veränderlichen. Fund. Math. 24, 1935, pp. 213-246. JFM 61.0541.02 | Zbl 0011.35202

2 K.O. Friediuchs, Sytmmetric Hyperbolic Linear Differential Equations. Comm. Pure Appl. Math. 7, 1954, pp. 345-392. MR 62932 | Zbl 0059.08902

3 I. Nash, The Imbedding of Riemannian Manifolds, Ann. Math. 63, 1956, pp. 20-63. Zbl 0070.38603

4 J. Schwartz, On Nash' s Implicit Function Theorem, Comm. Pure Appl. Math 13, 1960, pp. 509-530. MR 114144 | Zbl 0178.51002

4' J. Moser, 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 132859 | Zbl 0104.30503

4" J. Moser, On Invariant Curves of Area-Preserving Mappings of an Annulus. Nachr. Akad. Wiss. Göttingen Math. Phys. K1. IIa, No. 1, 1962, pp. 1-20. MR 147741 | Zbl 0107.29301

5 G.L. Siegel, Iteration of Analytic Functions. Ann. of Math. 43, 1942, pp. 647-612. MR 7044 | Zbl 0061.14904

5' C.L. Siegel, Über die Normalform Analytischer Differentialgleichungen in der Nähe einer Gleich-gewichtslösung, Nachr. Akad. Wiss., Göttingen, Math. Phys.K1, IIa, 1952, pp. 21-30. MR 57407 | Zbl 0047.32901

6 A.N. Kolmogorov, Doklad. Akad., Nauk USSR 98, 1954, pp. 527-530. MR 68687 | Zbl 0056.31502

7 A.N. Kolmogorov, General Theory of Dynamical Systeans and Classical Mechanics. Proc. of Intl. Congress of Math., Amsterdam, 1954, (Amsterdam: Erven P. Nordhoff, 1957), Vol. 1, pp. 315-333. Zbl 0095.17103

8 V.I. Arnold, @@ Small divisors » I, On mappings of a circle onto itself, Isvest. Akad. Nauk, ser. mat., 25, No. 1, 1961, pp. 21-76. MR 140699

9 V.I. Arnold, Small Divisor and Stability Problemis in Classicat and Celestial Mechanics. Uspekhi Mat. Nauk USSR, Vol. 18, Ser. 6 (119), 1963, pp. 81-192. MR 170705

10 V.I. Arnold, Proof of A. N. Kolmogorov's Theorem on the Preservation of Quasi-Periodic Motions under Small Perturbation of the Hamiltonian, Uspekhi Mat. N. USSR, Vol. 18, Ser. 5 (113), 1963, pp. 13-40. MR 163025 | Zbl 0129.16606

11 K.O. Friedrighs, Symmetric Positive Linear Differential Equations, Comm. Pure Appl. Math. 11, 1958, pp. 333-418. MR 100718 | Zbl 0083.31802

12 N.N. Bogolioubov, and Y.A. Mitropolski, The Method of Intergral Manifolds in Nonlinear Mechanics, Contrib. to Differential Equations, Vol. II, 1963, pp. 123-196. Zbl 0137.28406

13 S.P. Diliberto, Perturbation Theorems for Periodic Surfaces I, Rend. del Cire. Mat. Palermo (2), 9, 1961, pp. 265-299. II, Rend. del Circ. Mat. Palermo (2), 10, 1962, pp. 111 161. MR 142853 | Zbl 0109.31401

13' S.P. Diliberto, Perturbation 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 149038 | Zbl 0104.06303

14' J.K. Hale, Integral Manifolds of Perturbed Differential Systems, Annals of Math., 78. 1961, pp. 496-531. MR 123786 | Zbl 0163.32804

15 I. Kupka, Stabilité des varietés invariantes d'un champ de vecteurs pour les petites perturbations. Compt. Rend. Acad. Sc. Paris, 258, Group 1, 1964, pp. 4197-4200. MR 162036 | Zbl 0117.05403

16 L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), pp. 116-162. Numdam | MR 109940 | Zbl 0088.07601

17 Gagliardo, E., Ulteriori proprieta di alcune classi di funzioni in più variabili, Ricerche Mat, 8, 1959, pp. 24-51. MR 109295 | Zbl 0199.44701

18 J.J. Kohn and L. Nirenberg, Non-coercive boundary value problems to appear in Comm. Pure Appl. Math. (See under « elliptic regularization »). MR 181815 | Zbl 0125.33302

19 W.T. Kyner, A fixed point theorem. Contributions to the Theory on Vonlinear Oscillations, Vol. 3, Princeton University Press, Annals of Math. Studies 36, 1956, pp. 197-205. MR 81472 | Zbl 0073.33501

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 101946

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

22 C.L. Siegel, Verlesungen über Himmelsmechanik, Springer, 1956. MR 80009

23 H. Cremer, Über die Hänfigkeit der Niehtzentren, Math. Ann. 115, pp. 607-612, 1942. JFM 64.0289.02 | Zbl 0018.36802

24, N. Levinson, Transformation of an analytic function of several zariables to a canonical form. Duke Math. Journal 28, 1961, pp. 345-353. (See Theorem 2). MR 145101 | Zbl 0100.29002

25 N.I. Achieser, Vorlisungen iiber Approximationstheorie, Akd, Verlag. Berlin 1953, translated from Russian, Chapter V. MR 61692 | Zbl 0052.29002