The Krasnoselskii-Rabinowitz Bifurcation Theorem
Robert F. Brown · Birkhäuser Boston eBooks · 1993
In the previous chapter, we used spectral theory to make a computation of Leray-Schauder degree, thus combining two of the main topics of Part II. In this chapter, which presents the main result of the book, we’ll also be using the separation theorem from point-set topology that we proved in Chapter 11. However, we first need to introduce a hypothesis that permits us to apply the theory of compact linear operators in a more general, nonlinear, setting.