Topological Methods in the Study of Boundary Value Problems

Description

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. Front Matter....Pages i-xvi Shooting Type Methods....Pages 1-27 The Banach Fixed Point Theorem....Pages 29-51 Iterative Methods....Pages 53-82 The Schauder Theorem and Applications....Pages 83-107 Topological Degree: An Introduction....Pages 109-144 Applications....Pages 145-187 Back Matter....Pages 189-226