A homotopy method for solving an equation of the type - Δ u = F ( u )

Christophe Devys; Jean-Michel Morel; P. Witomski

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

  • Volume: 1, Issue: 4, page 205-222
  • ISSN: 0294-1449

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Devys, Christophe, Morel, Jean-Michel, and Witomski, P.. "A homotopy method for solving an equation of the type $- \Delta u = F(u)$." Annales de l'I.H.P. Analyse non linéaire 1.4 (1984): 205-222. <http://eudml.org/doc/78073>.

@article{Devys1984,
author = {Devys, Christophe, Morel, Jean-Michel, Witomski, P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Laplace equation; homotopy continuation method; Poisson equation; pseudo- inverse; pseudodeterminant},
language = {eng},
number = {4},
pages = {205-222},
publisher = {Gauthier-Villars},
title = {A homotopy method for solving an equation of the type $- \Delta u = F(u)$},
url = {http://eudml.org/doc/78073},
volume = {1},
year = {1984},
}

TY - JOUR
AU - Devys, Christophe
AU - Morel, Jean-Michel
AU - Witomski, P.
TI - A homotopy method for solving an equation of the type $- \Delta u = F(u)$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 4
SP - 205
EP - 222
LA - eng
KW - Laplace equation; homotopy continuation method; Poisson equation; pseudo- inverse; pseudodeterminant
UR - http://eudml.org/doc/78073
ER -

References

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  1. [1] Abraham- Robbin, Transversal Mappings and Flows. W. A. Benjamin, Inc., 1967. Zbl0171.44404MR240836
  2. [2] R.A. Adams, Sobolev Spaces. Academic Press, New York, 1975. Zbl0314.46030MR450957
  3. [3] J.C. Alexander and J.A. Yorke, A numerical continuation method that works generically. University of Maryland, Dept. of Math., MD 77-9, JA, TR 77-9, 1977. 
  4. [4] S.N. Chow, J. Mallet-Paret and J.A. Yorke, Finding zeros of maps: Homotopy methods that are constructive with probability one. Math. Comp., t. 32, 1978, p. 887-899. Zbl0398.65029MR492046
  5. [5] B.C. Eaves and R. Saigal, Homotopies for computation of fixed points on unbounded regions, Mathematical Programming, t. 3, n° 2, 1972, p. 225-237. Zbl0258.65060MR314028
  6. [6] T. Kato, Perturbation theory for nonlinear operators. Springer Verlag, 1966. Zbl0148.12601MR203473
  7. [7] R.B. Kellog, T.Y. Li and J. Yorke, A Method of Continuation for Calculating a Brouwer Fixed Point, in: Computing Fixed Points with Applications, S. Karamardian, ed., Academic Press, New York, 1977. Zbl0426.90094MR448864
  8. [8] S. Lang, Analysis, Madison-Wesley Publishing Company, 1968. Zbl0159.34303
  9. [9] S. Smale, An infinite dimensional version of Sard's theorem. American Journal of Math., t. 87, 1965, p. 861-866. Zbl0143.35301MR185604
  10. [10] S. Smale, A convergent process of price adjustment and global Newton methods, J. Math. Econ., t. 3, p. 1-14. Zbl0354.90018MR411577

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