Topological methods for discontinuous operators and applications

• Autores: Jorge Rodríguez
• Directores de la Tesis: Rubén Figueroa Sestelo (dir. tes.), Rodrigo López Pouso (codir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2020
• Idioma: español
• Tribunal Calificador de la Tesis: Petru Jebelean (presid.), Rosana Rodríguez López (secret.), José Ángel Cid Araújo (voc.)
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Ecuaciones funcionales
      • Transformadas integrales
      • Ecuaciones diferenciales ordinarias
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • 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.