Homotopy and Degree Theory

Antonio Villanacci, Laura Carosi, Pierluigi Benevieri and Andrea Battinelli
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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

Chapter Chapter 7 in Differential Topology and General Equilibrium with Complete and Incomplete Markets, 2002, pp 159-204 from Springer

Abstract: 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.

Keywords: Open Subset; Open Neighborhood; General Equilibrium; Neighborhood Versus; Tubular Neighborhood (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-3619-9_7

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DOI: 10.1007/978-1-4757-3619-9_7

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