A Topological Introduction to Nonlinear Analysis

Couverture
Springer Science & Business Media, 12 déc. 2003 - 184 pages

"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory . . . reading is fluid and very pleasant . . . style is informal but far from being imprecise."

—MATHEMATICAL REVIEWS (Review of the First Edition)

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.

New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book. * Several new proofs, making the second edition more self-contained.

 

Pages sélectionnées

Table des matières

The Topological Point of View
3
AscoliArzela Theory
9
Brouwer Fixed Point Theory
19
Schauder Fixed Point Theory
23
The Forced Pendulum
29
Equilibrium Heat Distribution
39
Generalized Bernstein Theory
45
Degree Theory
49
A Separation Theorem
95
Compact Linear Operators
99
The Degree Calculation
111
The KrasnoselskiiRabinowitz Bifurcation Theorem
119
Nonlinear SturmLiouville Theory
133
More SturmLiouville Theory
143
Euler Buckling
155
Appendices
161

Brouwer Degree
51
Properties of the Brouwer Degree
55
LeraySchauder Degree
63
Properties of the LeraySchauder Degree
69
The Mawhin Operator
79
The Pendulum Swings Back
85
Bifurcation Theory
93
Singular Homology
163
Additivity and Product Properties
169
Bounded Linear Transformations
175
References
181
Index
183
Droits d'auteur

Autres éditions - Tout afficher

A Topological Introduction to Nonlinear Analysis
Robert F. Brown
Aperçu limité - 2011
A Topological Introduction to Nonlinear Analysis
Robert F. Brown
Aperçu limité - 2013
A Topological Introduction to Nonlinear Analysis
Robert F. Brown
Aperçu limité - 2014
Tout afficher »

Expressions et termes fréquents

algebraic topology Ascoli-Arzela theorem assume Banach space bifurcation point boundary condition boundary value problem bounded subset Brouwer degree Cauchy chapter closed subset compact linear operator compact map compact set compact subset completely continuous contains continuous function convergent subsequence cross product defined definition denote differential equation euclidean space Euler buckling problem exists Figure finite finite-dimensional fixed point theorem forced pendulum equation Frechet differentiable function f h₁ Hn(S homology homomorphism homotopy homotopy property hypothesis implies integer interval isomorphism Lemma Leray-Schauder degree map f Mawhin operator metric space nonlinear Sturm-Liouville nonzero normed linear space null space open subset Proof prove real number relatively compact satisfy Schauder fixed point solution Sturm-Liouville problem subspace Suppose T-periodic tells theory topological totally bounded U₁ V₁ write X₁ zero λη λι μη

Références à ce livre

Informations bibliographiques

TitreA Topological Introduction to Nonlinear Analysis
AuteurRobert F. Brown
Édition2
ÉditeurSpringer Science & Business Media, 2003
ISBN0817632581, 9780817632588
Longueur184 pages
  
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