Topological methods for discontinuous operators and applications
- Rubén Figueroa Sestelo Director
- Rodrigo López Pouso Co-director
Defence university: Universidade de Santiago de Compostela
Fecha de defensa: 21 January 2020
- Petru Jebelean Chair
- Rosana Rodríguez López Secretary
- 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.