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Homotopy and Degree Theory

  • Antonio Villanacci
  • Laura Carosi
  • Pierluigi Benevieri
  • Andrea Battinelli
Chapter

Abstract

For almost a century, degree theory has been a very important tool in analysis of existence and multiplicity results for solutions to nonlinear equations in euclidean spaces and manifolds. For example, the study of ordinary and partial differential equations has been considerably improved by degree theory. From the point of view taken in the present chapter, we give a simplified account of the matter by saying that degree theory consists in giving an estimate of the number of solutions to the equation f (x) = y for a function f: MN, where M and N are C 2 boundaryless manifolds and f is continuous.

Keywords

Open Subset Open Neighborhood General Equilibrium Neighborhood Versus Tubular Neighborhood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Antonio Villanacci
    • 1
  • Laura Carosi
    • 2
  • Pierluigi Benevieri
    • 1
  • Andrea Battinelli
    • 3
  1. 1.Università degli Studi di FirenzeItaly
  2. 2.Università degli Studi di PisaItaly
  3. 3.Università degli Studi di SienaItaly

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