Degree theories

Abstract

Degree theory deals with an abstract equation of the form ϕ(u) = ξ. In many situations, we are interested not only in the existence of solutions for the equation, but also in their multiplicity. This is, for example, the case in bifurcation theory, where we want to determine the values of the parameter λ, where the number of solutions of an equation of the form ϕ(u, λ) = ξ changes.