Topological Methods in the Study of Boundary Value Problems

2014
ISBN: 978-1-4614-8892-7
Verlag: Springer US

Buch, Englisch, 226 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 3752 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Amster, Pablo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Topologie Analytische Topologie

Inhaltsverzeichnis

Introduction.- Shooting type methods.- The Banach Fixed Point Theorem.- Schauder’s Theorem and applications.- Topological degree: an introduction.- Applications.- Basic facts on metric and normed spaces.- Brief review of ODE’s.- Hints and Solutions to Selected Exercises.

Über Autor(innen)

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