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Homotopy and Degree Theory

In: Differential Topology and General Equilibrium with Complete and Incomplete Markets

Author

Listed:
  • Antonio Villanacci

    (Università degli Studi di Firenze)

  • Laura Carosi

    (Università degli Studi di Pisa)

  • Pierluigi Benevieri

    (Università degli Studi di Firenze)

  • Andrea Battinelli

    (Università degli Studi di Siena)

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: M → N, where M and N are C 2 boundaryless manifolds and f is continuous.

Suggested Citation

  • Antonio Villanacci & Laura Carosi & Pierluigi Benevieri & Andrea Battinelli, 2002. "Homotopy and Degree Theory," Springer Books, in: Differential Topology and General Equilibrium with Complete and Incomplete Markets, chapter 0, pages 159-204, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-3619-9_7
    DOI: 10.1007/978-1-4757-3619-9_7
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