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Proceedings of the American Mathematical Society

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A remark on expanding maps

Authors: Kung Ching Chang and Shu Jie Li
Journal: Proc. Amer. Math. Soc. 85 (1982), 583-586
MSC: Primary 47H15; Secondary 58C15
MathSciNet review: 660608
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Abstract: In this paper we discuss the following problem stated by L. Nirenberg: Let $ T$ be an expanding map $ H \to H$ ($ H$ is a Hilbert space) with $ T(0) = 0$. Suppose $ T$ maps a neighborhood of the origin onto a neighborhood of the origin. Does $ T$ map $ H$ onto $ H$?

We answer positively the problem when $ T$ is differentiable.

References [Enhancements On Off] (What's this?)

  • [1] L. Nirenberg, Topics in nonlinear functional analysis, Lecture Notes, Courant Inst., New York Univ., New York, 1974. MR 0488102 (58:7672)
  • [2] J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach, New York, 1969. MR 0433481 (55:6457)
  • [3] G. J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962). MR 0169064 (29:6319)
  • [4] F. Browder, On the Fredholm alternative for nonlinear operators, Bull. Amer. Math. Soc. 76 (1970), 993-998. MR 0265999 (42:908)
  • [5] M. M. Vainberg, Variational methods for the study of nonlinear operators, Holden-Day, San Francisco, Calif., 1964. MR 0176364 (31:638)

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Keywords: Expanding map, Hadamard implicit function theorem, potential operator
Article copyright: © Copyright 1982 American Mathematical Society

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