Topological methods for discontinuous operators and applications

  1. Jorge Rodríguez
Supervised by:
  1. Rubén Figueroa Sestelo Director
  2. Rodrigo López Pouso Director

Defence university: Universidade de Santiago de Compostela

Year of defence: 2020

Committee:
  1. Petru Jebelean Chair
  2. Rosana Rodríguez López Secretary
  3. José Ángel Cid Araújo Committee member

Type: Thesis

Abstract

The aim of this thesis will be to introduce and study a new generalization of the topological degree, which it coincides with the usual theory in the case of continuous operators, and that it allows the existence of discontinuities. As a consequence we will study the existence of fixed points for some types of non neccesarily continuous operators and we will apply it to the study of the existence of solutions for several types of differential problems (initial value problems and/or boundary value problems) with discontinuous ordinary differential equations of different orders.The objective will be to introduce and study a new generalization of the topological degree, which it coincides with the usual theory in the case of continuous operators, and that it allows the existence of discontinuities. As a consequence we will study the existence of fixed points for some types of non neccesarily continuous operators and we will apply it to the study of the existence of solutions for several types of differential problems (initial value problems and/or boundary value problems) with discontinuous ordinary differential equations of different orders.