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Solutions numériques de problèmes de bifurcation. (French) Zbl 0439.65087


MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
47J25 Iterative procedures involving nonlinear operators
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
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References:

[1] 1. C. BOLLEY, Etude numérique d’un problème de bifurcation, Thèse de 3e cycle, Rennes, 1977.
[2] 2. P. GRISVARD, Behavior of the Solutions of an Elliptic Boundary Value Problem in a Polygonal or Polyhedral Domain, Num. Sol of Partial Diff. Eq. III, 1976. Zbl0361.35022 MR466912 · Zbl 0361.35022
[3] 3. J. KITCHEN, Concerning the Convergence of Iterates to Fixed Points, Studia Math.,Vol. 27, 1966, p. 247-249. Zbl0143.16601 MR200759 · Zbl 0143.16601
[4] 4. P. H. RABINOWITZ, On Bifurcation From Infinity, J. of Diff. Eq., vol. 14, 1973, p. 462-475. Zbl0272.35017 MR328705 · Zbl 0272.35017
[5] 5. P. H. RABINOWITZ, Some Global Results for Nonlinear Eigenvalue Problems, J. Funct.Anal., vol. 7, 1971, p. 487-513. Zbl0212.16504 MR301587 · Zbl 0212.16504
[6] 6. D. SATTINGER, Stability of Bifurcating Solutions by Leray-Schauder Degree, Arch.R.M.A.-43, 1971, p. 154-166. Zbl0232.34027 MR336485 · Zbl 0232.34027
[7] 7. D. SATTINGER, Monotone Methods in Nonlinear Elliptic and Parabolic Boundary Value Problems, Indiana Univ. Math. J., vol. 21, n^\circ 11, 1972. Zbl0223.35038 MR299921 · Zbl 0223.35038
[8] 8. D. SATTINGER, Topics in Stability and Bifurcation Theory, Lecture Notes, n^\circ 309Spinger-Verlag. Zbl0248.35003 MR463624 · Zbl 0248.35003
[9] 9. I. STAKGOLD et L. E. PAYNE, Nonlinear Problems in Nuclear Reactor Analysis, Lecture Notes, n^\circ 322, Springer-Verlag. Zbl0259.35025 · Zbl 0259.35025
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