A rapid convergence method for a singular perturbation problem

Paul H. Rabinowitz

Annales de l'I.H.P. Analyse non linéaire (1984)

  • Volume: 1, Issue: 1, page 1-17
  • ISSN: 0294-1449

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Rabinowitz, Paul H.. "A rapid convergence method for a singular perturbation problem." Annales de l'I.H.P. Analyse non linéaire 1.1 (1984): 1-17. <http://eudml.org/doc/78066>.

@article{Rabinowitz1984,
author = {Rabinowitz, Paul H.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular perturbation; rapid convergence; existence; periodic solutions; approximate equation; elliptic regularization},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Gauthier-Villars},
title = {A rapid convergence method for a singular perturbation problem},
url = {http://eudml.org/doc/78066},
volume = {1},
year = {1984},
}

TY - JOUR
AU - Rabinowitz, Paul H.
TI - A rapid convergence method for a singular perturbation problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 1
SP - 1
EP - 17
LA - eng
KW - singular perturbation; rapid convergence; existence; periodic solutions; approximate equation; elliptic regularization
UR - http://eudml.org/doc/78066
ER -

References

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  1. [1] J. Nash, The embedding of Riemannian manifolds, Amer. Math., t. 63, 1956, p. 20-63. Zbl0070.38603MR75639
  2. [2] J. Moser, A rapidly converging iteration method and nonlinear partial differential equations I et II, Ann. Scuola Norm. Sup. Pisa, t. 20, 1966, p. 265-315 et p. 499-535. Zbl0144.18202
  3. [3] J.T. Schwartz, On Nash's implicit function theorem, Comm. Pure Appl. Math., t. 13, 1960, p. 509-530. Zbl0178.51002MR114144
  4. [4] F. Sergeraert, Un théorème de fonctions implicites sur certains espaces de Frechet et quelques applications, Ann. Sci. École Norm. Sup. (4e série), t. 5, 1972, p. 599-660. Zbl0246.58006MR418140
  5. [5] E. Zehnder, Generalized implicit function theorems with applications to some small divisor problems I et II, Comm. Pure Appl. Math., t. 28, 1975, p. 91-141 ; t. 29, 1976, p. 49-113. Zbl0309.58006MR380867
  6. [6] L. Hormander, Implicit function theorems, Stanford Univ., Lecture notes, 1977. 
  7. [7] R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. A. M. S. (new series), t. 7, 1982, p. 65-222. Zbl0499.58003MR656198
  8. [8] P.H. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential equations, II, Comm. Pure Appl. Math., t. 22, 1969, p. 15-39. Zbl0157.17301MR236504
  9. [9] W. Craig, A bifurcation theory for periodic dissipative wave equations. New York Univ. thesis, 1981, to appear Ann. Scuola Norm. Sup. Pisa. 
  10. [10] P.H. Rabinowitz, A curious singular perturbation problem, to appear Proc. Int. Conf. on Diff. Eq., Univ. of Alabama, Birmingham. Zbl0585.34033MR799385
  11. [11] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, Série 3, t. 13, 1959, p. 116-162. Zbl0088.07601MR109940
  12. [12] P.D. Lax, On Cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations, Comm. Pure Appl. Math., t. 8, 1955, p. 615-633. Zbl0067.07502MR78558
  13. [13] L. Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., t. 8, 1955, p. 648-674. Zbl0067.07602MR75415

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