Degree Theory in Analysis and Applications [Hardcover]

In recent years the need to extend the notion of degree to nonsmooth functions has been triggered by developments in nonlinear analysis and some of its applications. This new study relates several approaches to degree theory for continuous functions and incorporates newly obtained results for Sobolev functions. These results are put to use in the study of variational principles in nonlinear elasticity. Several applications of the degree are illustrated in the theories of ordinary and partial differential equations. Other topics include multiplication theorem, Hopf's theorem, Brower's fixed point theorem, odd mappings, and Jordan's separation theorem, all suitable for graduate courses in degree theory and application.

1. Degree theory for continuous functions
2. Degree theory in finite dimensional spaces
3. Some applications of the degree theory to Topology
4. Measure theory and Sobolev spaces
5. Properties of the degree for Sobolev functions
6. Local invertibility of Sobolev functions. Applications
7. Degree in infinite dimensional spaces
References
Index