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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Villanacci, A., Carosi, L., Benevieri, P., Battinelli, A. (2002). Homotopy and Degree Theory. In: Differential Topology and General Equilibrium with Complete and Incomplete Markets. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3619-9_7
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3619-9_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5306-3
Online ISBN: 978-1-4757-3619-9
eBook Packages: Springer Book Archive