Rubén Figueroa
Universidade de Santiago de Compostela

Abstract: The classical Leray-Schauder's degree is a very powerful tool in order to guarantee the existence of fixed points for suitable continuous operators in Banach spaces. As well-known, the solutions of a large class of boundary value problems can be written in terms of fixed points of continuous operators and so degree theory becomes very useful to deal with this kind of problems. However, Leray-Schauder's degree and the classical fixed point theorems fail when the corresponding mapping is discontinuous. In this talk we will develop a new degree theory for a certain class of operators that need not be continuous and we will show how this can be applied to Ordinary Differential Equations with discontinuous nonlinearities.