Zeidler E. — Nonlinear Functional Analysis and Its Applications: Part 1: Fixed-Point Theorems :: Электронная библиотека попечительского совета мехмата МГУ

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Zeidler E. — Nonlinear Functional Analysis and Its Applications: Part 1: Fixed-Point Theorems

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Название: Nonlinear Functional Analysis and Its Applications: Part 1: Fixed-Point Theorems

Автор: Zeidler E.

Аннотация:

This is the first of a five-volume exposition of the main principles of nonlinear functional analysis and
its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and
accessible to the nonspecialist. Among the topics of Volume I are the two basic fixed-point theorems of Banach and
Schauder, calculus in Banach spaces, the implicit function theorem, Newton`s method, analytic bifurcation theory,
fixed-point theorems for multivalued mappings, nonexpansive and condensing operators, mapping degree and fixed-point
index and their applications, analytic maps, and asymptotic fixed-point theorems.
The book contains numerous applications to such areas as ordinary and partial differential equations,
integral equations, and game theory. Many exercises and a comprehensive bibliography complement the text.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 897

Добавлена в каталог: 22.12.2011

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Предметный указатель

Retraction,trick for constructing fixed points      51 563
Riesz - Schauder theory for compact operators      372
Riesz - Schauder theory for dual pairs      788ff
Rotation of a vector field      521
Saddle point of a dynamical system      93
Saddle point of a functional      457
Scalar product      785
Schauder fixed-point theorem      56
Schauder fixed-point theorem, generalized      500 556 624 725
Schauder fixed-point theorem, second      452
Schauder fixed-point theorem, with uniqueness      624
Selection      463
Selection theorem, finite sets (marriage theorem)      464
Selection theorem, topological spaces (Michael's selection theorem)      466
Semi-linear      804
Semi-linear differential equation      see Applications to
Semi-linear operator equations      60 398
Separable B-space      770
Separable topological space      751
Separation theorem for compact sets      636
Separation theorem for convex sets      see Section 39.1 in Part III
Separation theorem Jordan - Brouwer      580
Sequentially closed      759
Sequentially compact      759
Sequentially complete      762
Set      746
Set theory      745ff
Set theory, basic theorems of      489 511 749
Set, absolutely convex      764
Set, absorbing      764
Set, algebraic      646
Set, analytic      646
Set, arcwise connected      758
Set, bounded      762 768 769 780
Set, Cantor      583 758
Set, circled      764
Set, closed      751
Set, compact      756
Set, connected      757
Set, convex      764
Set, dense      751
Set, directed      759
Set, finite      749
Set, infinite      749
Set, Julia      743
Set, locally arcwise connected      758
Set, massive      see Residual
Set, meager      see of first Baire category
Set, nowhere dense      751
Set, of first Baire category      802
Set, of normal structure      485
Set, of second Baire category      802
Set, open      751
Set, ordered      503
Set, perfect      754
Set, relatively closed      755
Set, relatively compact      756
Set, relatively open      755
Set, residual      802
Set, sequentially closed      759 760
Set, sequentially compact      759 760
Set, simply connected      758
Set, totally disconnected      757
Set, well-ordered      503
Sheaf theory      647; see Part V
Shift operator      86
Shockwaves      113
simplex      599
Singular fixed point      184
Singular point      184
Singular value      184
Singular zero      184
Small divisor      103 220 223
smallest      see Element
Sobolev space      261; see Part II
Space      800
Space, analytic      646ff
Space, arcwise connected      758
Space, Banach (B-space)      769
Space, Banach manifold      180
Space, barrelled      783
Space, bornological      783
Space, compact      756
Space, connected      757
Space, contractible      609
Space, covering      727; see Part V
Space, first countable      754
Space, fixed-point      609
Space, Fr $\acute{e}$ chet (F-space)      784
Space, function spaces      see List of Symbols
Space, Hausdorff      see Separated
Space, Hilbert (H-space)      785
Space, invariant      158
Space, Lebesgue      111
Space, Lindel $\ddot{o}$ f      757
Space, linear      763
Space, linear topological      see Topological space vector
Space, locally arcwise connected      758
Space, locally compact      597
Space, locally connected      757
Space, locally convex      779
Space, manifold      181
Space, metric      761
Space, metrizable      762
Space, normal      596
Space, nuclear      784; see Part V
Space, paracompact      597
Space, Polish      762
Space, regular      596
Space, second countable      754
Space, separable      751
Space, separated      754
Space, simply connected      758
Space, Sobolev      261
Space, topological      750
Space, topological vector      768
Space, totally disconnected      757
Spaces, schematic overviews of important      752 753
Spectral radius      795
Spectrum      795
Spectrum essential      497
Spectrum of compact operators      372
Splitting property      766
Stability of bifurcation solutions      386 424
Stability of biological equilibria      163
Stability of equilibrium points of dynamical systems      86
Stability of fixed points      158 160
Stability of fixed points of analytic maps      223
Stability of iterative methods      31 157 282
Stability of oscillations      91ff
Stability of periodic solutions      162 200 202
Stability of planetary system      100 125 222
Stability of positive solutions      282
Stability of solutions of elliptic equations      323 324
Stability of solutions of parabolic equations      330
Stability, notions of bifurcation solution (asymptotically stable, weakly asymptotically stable, unstable)      424
Stability, notions of equilibrium point (asymptotically stable, stable, unstable)      86
Stability, notions of fixed point (-stable, -weakly stable, -unstable)      160
Stability, notions of fixed point (asymptotically stable, stable, unstable)      158
Stability, notions of solution of an elliptic equation (asymptotically stable, weakly stable, unstable)      323 324
Stable homotopy      717
Stable manifold      93 112
Stable set      158
Stochastic particle reactions      124
Strange attractors      164
Strategy pair in game theory      461 462
Structural stability      95 99 100 106
Structure      800
Subimmersion      178
Subimmersion theorem      178

Submersion      183
Submersion Theorem      185
Support      756
Supremum in ordered sets      503
Suspension      715
Switching circuits      96
Symmetry in nature      109
Symplectic geometry      734; see Part V
Synergetics      656
Tangent      see Part IV
Tangent bundle      183
Tangent space      183
Tangential map      183 192;
Tangential map and the chain rule for higher derivatives      192
Taylor's theorem      148
Taylor's theorem, converse of      193
Theorem      see also Fixed-point theorem
Theorem, Alaoglu - Bourbaki      777 782
Theorem, approximation      55 533 770
Theorem, Arzel $\grave{a}$ - Ascoli      772
Theorem, Atiyah - J $\ddot{a}$ nich      727; see Part V
Theorem, Atiyah - Singer index      372 727;
Theorem, B $\acutez{e}$ zout      434
Theorem, Baire - Hausdorff      776 802
Theorem, Banach      111 779 782
Theorem, Banach - Steinhaus      111
Theorem, beer barrel      846
Theorem, Bernstein      246 251
Theorem, Bing - Nagata - Smimov metrization      597
Theorem, bipolar      see Part III
Theorem, Birkhoff - Kellogg      559
Theorem, Borsuk - Ulam      708
Theorem, Borsuk antipodal      701
Theorem, Borsuk homotopy extension      698
Theorem, Bott periodicity      727
Theorem, bread-ham-cheese      710
Theorem, Brouwer - Schauder invariance of domain      705
Theorem, Brouwer fixed-point index      535
Theorem, Brouwer invariance of dimension      581
Theorem, Brouwer mapping classes      692 711
Theorem, bunch      392
Theorem, Caccioppoli      174
Theorem, closed graph      779
Theorem, closed graph, nonlinear      471
Theorem, closed range      111
Theorem, Cohen independence      748 749
Theorem, Crandall - Rabinowitz      383 426
Theorem, Cronin - Schwartz      621
Theorem, curve selection      639 647
Theorem, Dancer - Turner      669
Theorem, Eberlein- $\check{S}$ muljan      111
Theorem, embedding      233
Theorem, Euler polyhedral      727; see Part V
Theorem, extension      see Extension of
Theorem, for semi-linear equations      398
Theorem, Frobenius      167 343
Theorem, G $\ddot{o}$ del incompleteness      749
Theorem, Gauss - Bonnet - Chern      727; see Part V
Theorem, general mean value      76
Theorem, generalized Frobenius      167
Theorem, generalized Gronwall      281
Theorem, generalized Peano      81
Theorem, generalized Picard - Lindelof      78
Theorem, generalized Taylor      148
Theorem, Grobman - Hartman      100
Theorem, Gronwall      82
Theorem, Grundmann      421ff 640
Theorem, Hadamard      174
Theorem, Hahn - Banach      776
Theorem, hard implicit function theorem (Moser - Nash)      218
Theorem, Hausdor      ff
Theorem, hedgehog      see Poincare - Brouwer
Theorem, Hess - Kato      347
Theorem, Hopf classification      711
Theorem, implicit function      150
Theorem, invariance of domain      705
Theorem, inverse mapping theorem, global      174
Theorem, inverse mapping theorem, local      172
Theorem, Ize      669
Theorem, Jentzsch      291
Theorem, Jordan - Brouwer separation      580
Theorem, Jordan curve      581 592
Theorem, Kantorovi $\check{c}$       210
Theorem, Knaster- Kurato wski- M azurkiewicz      67
Theorem, Kneser - Fukuhara      567
Theorem, Krasnoselskii - Zabreiko - Steinlein mod       724
Theorem, Krasnoselskii cone expansion      562
Theorem, Krasnoselskii local bifurcation      666
Theorem, Krasnoselskii monotone minorant      286
Theorem, Krein - Milman      see Section 38.7 in Part III)
Theorem, Krein - Rutman      290
Theorem, Krein - Smuljan      782
Theorem, Leray - Schauder continuation      245 556 628
Theorem, Leray - Schauder fixed-point index      542
Theorem, Leray - Schauder unbounded component      631
Theorem, Leray- Schauder index      619
Theorem, Leray-product      575
Theorem, Ljapunov center      655; see Part IV
Theorem, Ljapunov stability      87 99
Theorem, Ljusternik - Schnirelman - Borsuk      708
Theorem, Mackey - Arens      see Part III
Theorem, marriage      464
Theorem, Mazur      776
Theorem, Menger - N $\ddot{o}$ beling embedding      594
Theorem, Michael selection      466
Theorem, Milman      475
Theorem, minimax      458
Theorem, Moser - Nash      218
Theorem, Moser twist      736
Theorem, Nagumo      122
Theorem, Nash embedding      220
Theorem, Nash equilibrium      469
Theorem, Noether      110; see Part V
Theorem, nonlinear Krein - Rutman      312
Theorem, on generic finiteness      189
Theorem, on transflnite induction      511
Theorem, open mapping      111
Theorem, open mapping, nonlinear      705
Theorem, parametrized Sard      188
Theorem, Peano      57
Theorem, Perron      291 342
Theorem, Picard - Lindel $\ddot{o}$ f      27
Theorem, Poincar $\acute{e}$ - Alexander duality      581 727;
Theorem, Poincar $\acute{e}$ - Bendixson      120
Theorem, Poincar $\acute{e}$ - Bohl      571
Theorem, Poincar $\acute{e}$ - Brouwer      558
Theorem, Poincar $\acute{e}$ - Hopf      727; see Part V
Theorem, preimage      185
Theorem, Rabinowitz global bifurcation      668
Theorem, rank      178 195
Theorem, Riemann - Roch      727; see Part V
Theorem, Riesz compactness      111
Theorem, Riesz representation      785
Theorem, Sard      186 550
Theorem, Sard - Smale      186 550
Theorem, separation      see Separation
Theorem, Siegel center      223
Theorem, Smale complexity      257
Theorem, Spectral Mapping      798
Theorem, Sturm oscillation      792
Theorem, subimmersion      178
Theorem, Submersion      185
Theorem, Sundman      125
Theorem, surjective implicit function      177
Theorem, Taylor      148
Theorem, Tietze - Dugundji      49 65 756
Theorem, Tietze - Urysohn      756
Theorem, Tihonov product      756
Theorem, uniform boundedness      111
Theorem, Urysohn metrization      596

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