A simple intuitive proof of a theorem in degree theory for gradient mappings
Author:
James C. Scovel
Journal:
Proc. Amer. Math. Soc. 93 (1985), 751753
MSC:
Primary 55M25; Secondary 58C05, 58E05
MathSciNet review:
776215
Fulltext PDF Free Access
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Abstract: We give a simple, intuitive proof of a known theorem: the degree of the gradient of a coercive functional on a large ball in is one.
 [H]
Herbert
Amann, A note on degree theory for gradient
mappings, Proc. Amer. Math. Soc.
85 (1982), no. 4,
591–595. MR
660610 (83i:47069), http://dx.doi.org/10.1090/S00029939198206606102
 [M]
M.
A. Krasnosel′skiĭ, The operator of translation along
the trajectories of differential equations, Translations of
Mathematical Monographs, Vol. 19. Translated from the Russian by Scripta
Technica, American Mathematical Society, Providence, R.I., 1968. MR 0223640
(36 #6688)
 [J]
John
W. Milnor, Topology from the differentiable viewpoint, Based
on notes by David W. Weaver, The University Press of Virginia,
Charlottesville, Va., 1965. MR 0226651
(37 #2239)
 [L]
L.
Nirenberg, Variational and topological methods in
nonlinear problems, Bull. Amer. Math. Soc.
(N.S.) 4 (1981), no. 3, 267–302. MR 609039
(83e:58015), http://dx.doi.org/10.1090/S027309791981148886
 [P]
Paul
H. Rabinowitz, A note on topological degree for potential
operators, J. Math. Anal. Appl. 51 (1975),
no. 2, 483–492. MR 0470773
(57 #10518)
 [E]
Erich
H. Rothe, A relation between the type numbers of a critical point
and the index of the corresponding field of gradient vectors, Math.
Nachr. 4 (1951), 12–17. MR 0040597
(12,720c)
 [H]
 Amann, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc. 85 (1982), 591595. MR 660610 (83i:47069)
 [M]
 A. Krasnosel'skii, The operator of translation along the trajectories of differential equations, Transl. Math. Monos., vol. 19, Amer. Math. Soc., Providence, R.I., 1968. MR 0223640 (36:6688)
 [J]
 W. Milnor, Topology from a differentiable viewpoint, Univ. Press of Virginia, Charlottesville, Va., 1965. MR 0226651 (37:2239)
 [L]
 Nirenberg, Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 267302. MR 609039 (83e:58015)
 [P]
 H. Rabinowitz, A note on topological degree for potential operators, J. Math. Anal. Appl. 51 (1975), 483492. MR 0470773 (57:10518)
 [E]
 H. Rothe, A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors, Math. Nachr. 4 (195051), 1227. MR 0040597 (12:720c)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198507762151
PII:
S 00029939(1985)07762151
Article copyright:
© Copyright 1985
American Mathematical Society
