A Topological Introduction to Nonlinear Analysis

• Κύριος συγγραφέας: Brown, Robert F. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
• Έκδοση: 3rd ed. 2014.
• Θέματα: Mathematics.; Functional analysis.; Differential equations.; Partial differential equations.; Topology.; Functional Analysis.; Ordinary Differential Equations.; Partial Differential Equations.

 This third edition of A Topological Introduction to Nonlinear Analysis is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. For this third edition, several new chapters present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer:  written in a very personal, eloquent and instructive style it makes  one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006). 

 Preface -- Part I Fixed Point Existence Theory -- The Topological Point of View -- Ascoli-Arzela Theory -- Brouwer Fixed Point Theory -- Schauder Fixed Point Theory -- The Forced Pendulum -- Equilibrium Heat Distribution -- Generalized Bernstain Theory -- Part II Degree Theory -- Brouwer Degree -- Properties of the Brouwer Degree -- Leray-Schauder Degree -- Properties of the Leray-Schauder Degree -- The Mawhin Operator -- The Pendulum Swings back -- Part III Fixed Point Index Theory -- A Retraction Theorum -- The Fixed Point Index -- The Tubulur Reactor -- Fixed Points in a Cone -- Eigenvalues and Eigenvectors -- Part IV Bifurcation Theory -- A Separation Theorem -- Compact Linear Operators -- The Degree Calculation -- The Krasnoselskii-Rabinowitz Theorem -- Nonlinear Strum Liouville Theory -- More Strum Liouville Theory -- Euler Buckling -- Part V Appendices.