Degree Theory in Analysis and Applications (Oxford Lecture Series in Mathematics and Its Applications, 2)

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. This text examines degree theory and some of its applications in analysis. Topics described include: degree theory for continuous functions; the multiplication theorem; Hopf's theorem; Brower's fixed point theorem; odd mappings; and Jordan's separation theorem.