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- catalog abstract "Here is a book that will be a joy 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. 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.".
- catalog contributor b13105851.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description "Here is a book that will be a joy 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. 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.".
- catalog description "Includes bibliographical references (p. [181]) and index.".
- catalog description "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 Bernstein Theory -- Part II: Degree Theory -- Brouwer Degree -- Leray-Schauder Degree -- Properties of the Leray-Schauder Degree -- The Mawhin Operator -- The Pendulum Swings Back -- Part III: Bifurcation Theory -- A Separation Theorem -- Compact Linear Operators -- The Degree Calculation -- The Krasnoselskii-Rabinowitz Bifurcation Theorem -- Nonlinear Sturm-Liouville Theory -- Euler Buckling -- Part IV: Appendices -- Singular Homology -- Additivity and Product Properties -- Bounded Linear Transformations -- References -- Index.".
- catalog extent "xi, 184 p. :".
- catalog hasFormat "Topological introduction to nonlinear analysis.".
- catalog identifier "0817632581 (alk. paper)".
- catalog identifier "3764332581 (Basel : alk. paper)".
- catalog isFormatOf "Topological introduction to nonlinear analysis.".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "eng".
- catalog publisher "Boston : Birkhäuser,".
- catalog relation "Topological introduction to nonlinear analysis.".
- catalog subject "515/.7 22".
- catalog subject "Differential Equations.".
- catalog subject "Differential equations, partial.".
- catalog subject "Functional analysis.".
- catalog subject "Mathematics.".
- catalog subject "Nonlinear functional analysis.".
- catalog subject "QA321.5 .B79 2004".
- catalog subject "Topology.".
- catalog tableOfContents "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 Bernstein Theory -- Part II: Degree Theory -- Brouwer Degree -- Leray-Schauder Degree -- Properties of the Leray-Schauder Degree -- The Mawhin Operator -- The Pendulum Swings Back -- Part III: Bifurcation Theory -- A Separation Theorem -- Compact Linear Operators -- The Degree Calculation -- The Krasnoselskii-Rabinowitz Bifurcation Theorem -- Nonlinear Sturm-Liouville Theory -- Euler Buckling -- Part IV: Appendices -- Singular Homology -- Additivity and Product Properties -- Bounded Linear Transformations -- References -- Index.".
- catalog title "A topological introduction to nonlinear analysis / Robert F. Brown.".
- catalog type "text".