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Some simple but representative problems in nonlinear analysis are studied
Only basic knowledge of main topics in general analysis is needed, making the book easy-to-understand for non-specialists too
Concise and informal style, thus allowing also undergraduate students to enjoy some of the beauties of this interesting field of Mathematics
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.
Content Level »Graduate
Keywords »Boundary value problems - Fixed point theorems - Nonlinear analysis - Topological degree - Topological methods
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.