Local mapping relations and global implicit function theorems

Author:
Werner C. Rheinboldt

Journal:
Trans. Amer. Math. Soc. **138** (1969), 183-198

MSC:
Primary 46.90; Secondary 54.00

DOI:
https://doi.org/10.1090/S0002-9947-1969-0240644-0

MathSciNet review:
0240644

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References | Similar Articles | Additional Information

**[1]**Felix E. Browder,*The solvability of non-linear functional equations*, Duke Math. J.**30**(1963), 557–566. MR**156204****[2]**Lamberto Cesari,*The implicit function theorem in functional analysis*, Duke Math. J.**33**(1966), 417–440. MR**200754****[3]**D. F. Davidenko,*An application of the method of variation of parameters to the construction of iterative formulas of increased accuracy for numerical solutions of nonlinear equations*, Dokl. Akad. Nauk SSSR**162**(1965), 702-706 = Soviet Math. Dokl.**6**(1965), 702-706.**[4]**J. Davis,*The solution of nonlinear operator equations with critical points*, Tech. Rep. 25, Dept. of Math., Oregon State Univ., Corvallis, 1966.**[5]**Hans H. Ehrmann,*On implicit function theorems and the existence of solutions of non-linear equations*, Enseign. Math. (2)**9**(1963), 129–176. MR**156175****[6]**F. A. Ficken,*The continuation method for functional equations*, Comm. Pure Appl. Math.**4**(1951), 435–456. MR**45308**, https://doi.org/10.1002/cpa.3160040405**[7]**Hadamard,*Sur les transformations ponctuelles*, Bull. Soc. Math. France**34**(1906), 71–84 (French). MR**1504541****[8]**T. H. Hildebrandt and Lawrence M. Graves,*Implicit functions and their differentials in general analysis*, Trans. Amer. Math. Soc.**29**(1927), no. 1, 127–153. MR**1501380**, https://doi.org/10.1090/S0002-9947-1927-1501380-6**[9]**P. Lévy,*Sur les fonctions de lignes implicites*, Bull. Soc. Math. France**48**(1920), 13–27 (French). MR**1504790****[10]**Gunter H. Meyer,*On solving nonlinear equations with a one-parameter operator imbedding*, SIAM J. Numer. Anal.**5**(1968), 739–752. MR**242366**, https://doi.org/10.1137/0705057**[11]**George J. Minty,*Monotone (nonlinear) operators in Hilbert space*, Duke Math. J.**29**(1962), 341–346. MR**169064****[12]**Horst Schubert,*Topologie*, B. G. Teubner, Stuttgart, 1975 (German). Eine Einführung; Vierte Auflage; Mathematische Leitfäden. MR**0423277****[13]**J. T. Schwartz,*Nonlinear functional analysis*, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher; Notes on Mathematics and its Applications. MR**0433481****[14]**M. N. Yakovlev,*On the solution of systems of nonlinear equations by differentiation with respect to a parameter*, U.S.S.R. Comput. Math. and Math. Phys.**4**(1964), 146-149.

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DOI:
https://doi.org/10.1090/S0002-9947-1969-0240644-0

Article copyright:
© Copyright 1969
American Mathematical Society