Topological Methods in the Study of Boundary Value Problems

1. Front Matter

   Pages i-xvi

   PDF

2. Shooting Type Methods

   • Pablo Amster

   Pages 1-27

3. The Banach Fixed Point Theorem

   • Pablo Amster

   Pages 29-51

4. Iterative Methods

   • Pablo Amster

   Pages 53-82

5. The Schauder Theorem and Applications

   • Pablo Amster

   Pages 83-107

6. Topological Degree: An Introduction

   • Pablo Amster

   Pages 109-144

7. Applications

   • Pablo Amster

   Pages 145-187

8. Back Matter

   Pages 189-226

   PDF

This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.

• Boundary value problems
• Fixed point theorems
• Nonlinear analysis
• Topological degree
• Topological methods
• ordinary differential equations
• partial differential equations

“This book reviews in a nice and well-written way the most important topological methods in the study of boundary value problems associated to ordinary differential equations. It is understandable even with a minimal knowledge of functional analysis; as a consequence, it is useful for many readers, starting from Master’s degree students and up to experienced researchers, who will appreciate this thorough and self- contained description of the basic concepts in this field.” (Anna Capietto, zbMATH 1319.34001, 2015)

• Departamento de Matemática, FCEN-Universidad de Buenos Aires and IMAS-CONICET, Buenos Aires, Argentina

  Pablo Amster

Pablo Amster is an Associate Professor at the Department of Mathematics in Universidad de Buenos Aires, Argentina.

Policies and ethics