A Topological Introduction to Nonlinear AnalysisSpringer, 27 nov. 2014 - 240 pages This third edition 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. Included in this new edition are several new chapters that 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) |
Table des matières
Part II Degree Theory | 53 |
Part III Fixed Point Index Theory | 101 |
Part IV Bifurcation Theory | 136 |
A Singular Homology | 211 |
B Additivity and Product Properties | 217 |
C Bounded Linear Operators | 223 |
D Metric Implies Paracompact | 228 |
References | 233 |
Table of Symbols | 234 |
| 235 | |
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Expressions et termes fréquents
Ascoli-Arzela theorem B₁ Banach space bifurcation point boundary conditions boundary value problem bounded subset Brouwer degree Cauchy Chap chapter choose closed subset compact linear operator compact map compact set compact subset completely continuous contains continuous function convergent subsequence convex subset defined definition deg(I denote differential equation disjoint eigenvalue euclidean space exists finite finite-dimensional fixed point index fixed point theorem Frechet differentiable Fredholm operator function f homology homomorphism homotopy homotopy property hypothesis implies integer International Publishing Switzerland Introduction to Nonlinear isomorphism Lemma Leray-Schauder degree map ƒ Mawhin operator metric space Nonlinear Analysis nonlinear Sturm-Liouville normed linear space open subset Proof prove Publishing Switzerland 2014 R.F. Brown real number relatively compact satisfy sequence solution Springer International Publishing Sturm-Liouville problem subspace Suppose Switzerland 2014 R.F. tells theory Topological Introduction U₁ write zero