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Degree Theory for Discontinuous Operators

Applications to Discontinuous Differential Equations

  • Book
  • © 2021

Overview

Authors:
  1. Rubén Figueroa Sestelo

    1. IES Pedras Rubias Salceda de Caselas, Pontevedra, Spain

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  2. Rodrigo López Pouso

    1. Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela La Coruña, Spain

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  3. Jorge Rodríguez López

    1. Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela La Coruña, Spain

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  • This book opens a novel and fruitful line of research based on a generalized degree theory
  • Expands available techniques employed to prove existence of solutions for discontinuous problems
  • Presents many potential applications to other fields

Part of the book series: RSME Springer Series (RSME, volume 6)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López
    Pages 1-4

  3. Degree Theory for a Class of Discontinuous Operators

    • Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López
    Pages 5-23

  4. Fixed Point Theorems for Some Discontinuous Operators

    • Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López
    Pages 25-43

  5. First Order Problems

    • Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López
    Pages 45-82

  6. Second Order Problems and Lower and Upper Solutions

    • Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López
    Pages 83-133

  7. Positive Solutions for Second and Higher Order Problems

    • Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López
    Pages 135-179

  8. Back Matter

    Pages 181-190
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Keywords

About this book

This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder’s. Finally, readers will find in this book several applications of those discontinuous fixed-point theorems in the proofs of new existence results for discontinuous differential problems. Written in a clear, expository style, with the inclusion of many examples in each chapter, this book aims to be useful not only as a self-contained reference for mature researchers in nonlinear analysis but also for graduate students looking for a quick accessible introduction to degree theory techniques for discontinuous differential equations.

Reviews

“The monograph is perfectly organized and very well written. It provides a detailed presentation and insight on this new extension of the degree theory and illustrates the applicability of this tool in several problems. For these reasons, this book is suitable for researchers willing to learn more on this interesting topic.” (Guglielmo Feltrin, zbMATH 1505.47003, 2023)

Authors and Affiliations

  • IES Pedras Rubias Salceda de Caselas, Pontevedra, Spain

    Rubén Figueroa Sestelo

  • Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela La Coruña, Spain

    Rodrigo López Pouso, Jorge Rodríguez López

About the authors

Rubén Figueroa (Salvaterra de Miño, Galicia, 1984) obtained his Ph.D. degree at University of Santiago de Compostela in 2011, with a dissertation about discontinuous differential equations with deviated arguments. In the following years, he focused his research on the study of topological methods for discontinuous operators and its applications to Ordinary Differential Equations. This research gave rise to a score of scientific publications in different journals. At present, he combines his research with teaching at a secondary school.

Rodrigo López Pouso (Ferrol, Galicia, 1973) obtained his Ph.D. degree in 1999 with a thesis on discontinuous differential equations. He currently works as a professor at the University of Santiago de Compostela. His research interests range from discontinuous ordinary differential equations to classical real analysis and he is the author or co-author of more than 60 papers published in high impact mathematical journals.

Jorge Rodríguez-López (A Pontenova, Galicia, 1993) obtained a Ph.D. Degree in Mathematical Analysis at University of Santiago de Compostela in 2020. His line of research focuses on nonlinear analysis, with emphasis in discontinuous differential equations, topological methods and fixed point theory. His results on existence, uniqueness and multiplicity of solutions for ordinary differential equations have been published in several research papers included in the Citation Index Report. Currently, he is Assistant Professor at the University of Santiago de Compostela.

Bibliographic Information

  • Book Title: Degree Theory for Discontinuous Operators

  • Book Subtitle: Applications to Discontinuous Differential Equations

  • Authors: Rubén Figueroa Sestelo, Rodrigo López Pouso, Jorge Rodríguez López

  • Series Title: RSME Springer Series

  • DOI: https://doi.org/10.1007/978-3-030-81604-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-81603-2Published: 22 September 2021

  • Softcover ISBN: 978-3-030-81606-3Published: 23 September 2022

  • eBook ISBN: 978-3-030-81604-9Published: 21 September 2021

  • Series ISSN: 2509-8888

  • Series E-ISSN: 2509-8896

  • Edition Number: 1

  • Number of Pages: VIII, 190

  • Number of Illustrations: 9 illustrations in colour

  • Topics: Analysis

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