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Approximation of solution branches of nonlinear equations. (English) Zbl 0505.65016


MSC:

65J15 Numerical solutions to equations with nonlinear operators
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
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[1] [1] F BREZZI, J APPAZ and P A RAVIART, Finite Dimensional Approximation of Nonlinear Problems, Part I Branches of Nonsingular Solutions, Numer Math 36, 1980, 1-25 Zbl0488.65021 MR595803 · Zbl 0488.65021
[2] [2] F BREZZI, J RAPPAZ and P A RAVIART, Finite Dimensional Approximation of Nonlinear Problems, Part II Limit Points, Numer Math , 37, 1981, 1-28. Zbl0525.65036 MR615889 · Zbl 0525.65036
[3] [3] F BREZZI, J RAPPAZ and P A RAVIART, Finite Dimensional Approximation of Nonlinear Problems, Part III Simple Bifurcation Points, Numer Math , 38, 1981, 1-30 Zbl0525.65037 MR634749 · Zbl 0525.65037
[4] PG CIARLET, The Finite Element Method for Elliptic Problems, Studies in Mathe-matics and its Applications, Vol 4, North-Holland, 1978 Zbl0383.65058 MR520174 · Zbl 0383.65058
[5] D W DECKER and H B KELLER, Multiple Limite Point Bifurcation Report of Math Dept, California Institute of Technology, 1979
[6] J DESCLOUX, M LUSKIN and J RAPPAZ, Approximation of the Spectrum of Closed Operators The Determination of Normal Modes of a Rotating Basin, Math Comp, 36, 1981, 137-154 Zbl0458.65084 MR595047 · Zbl 0458.65084
[7] J DESCLOUX, N NASSIE and J RAPPAZ, On Spectral Approximation, RAIRO Numerical Analysis, 191, 137-154 Zbl0393.65024 · Zbl 0393.65024
[8] J DESCLOUX and J RAPPAZ, On Numerical Approximation of Solution Branches of Nonhnear Equations, Rapport, , Departement de Mathématiques, EPFL, 1981
[9] [9] J DESCLOUX and J RAPPAZ, Numerical Approximation of a Nonlinear Sturm-Liouville Problem on an Infinité Interval, to appear m the Proceedings of Equa-diff V, Teubner Zbl0514.65068 · Zbl 0514.65068
[10] R J MAGNUS, On the Local Structure of the Zero-Set of a Banach Space Valued Mapping , J Functional Analysis, 22, 1976, 58-72 Zbl0321.47042 MR418149 · Zbl 0321.47042
[11] [11] J -C PAUMIER, Une methode numérique pour le calcul des points de retournement Application a un problème aux limites non-lineaire II Analyse numérique d’un problème aux limites non-lineaire, Numer Math , 37, 1981, 445-454 Zbl0449.65025 MR627116 · Zbl 0449.65025
[12] J RAPPAZ and G RAUGEL, Finite Dimensional Approximation of Bifurcation Problems at a Multiple Eigenvalue, Rapport no 71, Centre de Mathématiques appliquées, Ecole Polytechnique, Palaiseau, 1981 · Zbl 0571.65048
[13] J RAPPAZ and G RAUGEL, Approximation of Double Bifurcation Points for Nonlinear Eigenvalue Problems, MAFELAP 1981 (Ed J Whiteman), Academic Press (to appear) Zbl0571.65048 · Zbl 0571.65048
[14] D H SATTINGER, Group Theorie Methods in Bifurcation Theory, Lecture Notes in Mathematics 762, Springer-Verlag, Berlin, 1979 Zbl0414.58013 · Zbl 0414.58013
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