Appendix. Degree Theory

  • Stuart S. Antman
Part of the Applied Mathematical Sciences book series (AMS, volume 107)


Throughout this section, we take Ω to be a bounded open subset of ℝ n and take cl Ω ∋ × → f(x) ∈ ℝ n to be continuous. We wish to estimate the number of solutions x in cl Ω of the equation
$$f(x) = 0.$$
We shall often be content with demonstrating that there is (at least) one solution. We denote the collection of solutions of (1.1) lying in c152 by f−1 ({0}).


Degree Theory Solution Pair Homotopy Invariance Real Normed Space Cofactor Matrix 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Stuart S. Antman
    • 1
  1. 1.Department of Mathematics and Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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