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

Dense set in a B-space      769
Derivative, basic ideas      131
Derivative, F-derivative      135
Derivative, G-derivative      135
Derivative, nth order      136
Derivative, of vector functions of one real variable      76
Derivative, partial      140
Diameter      762
Diffeomorphism      171
Diffeomorphism, e-diffeomorphism      172
Diffeomorphism, local      171
Differential calculus, basic ideas      131
Differential calculus, on Banach manifolds      181ff; see Parts IV and V
Differential equation, ordinary      see Ordinary
Differential equation, partial      see Applications to
Differential equation, quasi-linear      804
Differential equation, semi-linear      804
Differential inclusion      468
Differential topology      188 253 663;
Differential, basic ideas      131
Differential, F-differential      135
Differential, G-differential      135
Differential, nth order      143
Dimension of a linear space      765
Dimension of a manifold      181
Dimension of a set in a topological space      593 595
Dimension theory      593ff
Direct sum      765
Direct sum, topological      766
Discontinuum      594
Discontinuum, Cantor      583 594
Domain of definition      748
Dual B-space      774
Dual operator      775
Dual order cone      344
Dual pair      788
Duality in B-spaces      774
Duffing equation for nonlinear oscillations      738
Dynamical systems      see Ordinary differential equations and Part V
Dynamical systems, basic ideas      91ff
Dynamical systems, discrete      158
Dynamical systems, dissipative      725
Dynamical systems, stability      86ff 99 112 158
E-diffeomorphism      172
e-homeomorphism      755
Eigenray      420 641
Eigenspace (identical with space of eigenvectors)      269
Eigenspace (identical with space of eigenvectors), generalized complex      799
Eigenspace (identical with space of eigenvectors), generalized real      799
Eigenvalue      269
eigenvalue problems      see Bifurcation
Eigenvalue problems, boundary-eigenvalue problems for differential equations      326 344 347 389 671 682 791ff
Eigenvalue problems, integral equations      288 316 387 670 790ff
Eigenvalue problems, iterative methods for      40
Eigenvalue problems, Newton's method for      215
Eigenvalue problems, operators, linear (Hilbert - Schmidt theory and Riesz - Schauder theory)      372 790
Eigenvalue problems, operators, nonlinear      286 387 557 603ff
Eigenvalue problems, periodic solutions      408 413 438
Eigenvalue problems, positive matrices (Frobenius - Perron theory)      342ff
Eigenvalue problems, positive operators, linear (Krein- Rutman theory)      289
Eigenvalue problems, positive operators, nonlinear      286 312 388
Eigenvalue problems, systems of real equations      288 387 669
Eigenvector      269
Element in an ordered set, greatest      503
Element in an ordered set, maximal      503
Element in an ordered set, minimal      503
Element in an ordered set, smallest      503
Elementary particles      66 109 729 735;
Elliptic equations, classification, linear      258
Elliptic equations, classification, quasi-linear      804
Elliptic equations, classification, semi-linear      804
Elliptic equations, classification, strongly      234 258
Elliptic equations, classification, uniformly      246
Elliptic equations, linear, $C^{\alpha}$ -theory      259
Elliptic equations, linear, $L_{p}$ theory      261
Elliptic equations, linear, complementing condition      258 262
Elliptic equations, linear, functional-analytic approach to      235
Elliptic equations, linear, generalized solutions      236
Elliptic equations, linear, main theorems      257ff
Elliptic equations, linear, method of a priori estimates      235
Elliptic equations, linear, parametrix method      264
Elliptic equations, linear, symbol      258
Elliptic equations, quasi-linear      see Applications to
Elliptic equations, semi-linear      see Applications to
Ellipticity      246
Embedding      233
Embedding, compact      233
Embedding, continuous      233
Embedding, diffeomorphism (e-diffeomorphism)      172
Embedding, homeomorphism (e-homeomorphism)      755
Embedding, operator      233
Embedding, theorem for $C^{k, \alpha}$ -spaces      232
Embedding, theorem of Nash      220
ENR (euclidean neighborhood retract)      609
Entourage      800
entropy      656 (see also Parts IV and V)
Entropy principle (Brezis - Browder principle)      515 (see also Section 38.11 in Part III)
Epidemics      125
Equicontinuous      772 783
Equilibrium point at the end of trajectories      256
Equilibrium point in biology      162
Equilibrium point in chemistry      119
Equilibrium point in economics      255 (see also Part IV)
Equilibrium point index of an      95
Equilibrium point Nash      469 (see also Part IV)
Equilibrium point of a dynamical system      86 94ff 99
Equilibrium point of a dynamical system, asymptotically stable      87
Equilibrium point of a dynamical system, center      95
Equilibrium point of a dynamical system, hyperbolic      95 99
Equilibrium point of a dynamical system, node      94
Equilibrium point of a dynamical system, saddle point      93 94
Equilibrium point of a dynamical system, stable      86
Equivalent norm      772
Error estimates a posteriori      17 20
Error estimates a priori      17 20
Error estimates two-sided      8 300 301
Essential spectrum      497
Euler characteristic      609; see Part V
Excision property of fixed-pbint index      530
Excision property of mapping degree      570
Existence principle, and a priori estimates      227
Existence principle, basic ideas      7
Existence principle, essential maps and      693ff 715
Existence principle, fixed-point index and      520 529
Existence principle, for bifurcation points      657
Existence principle, for differential equations      see Applications to
Existence principle, for eigenvalues      286 557
Existence principle, for equations with operators of monotone type      300
Existence principle, for extrema      456 760
Existence principle, for fixed points      529 555
Existence principle, for global homeomorphistns      174 626 705 706
Existence principle, for global solutions of ordinary differential equations      79
Existence principle, for integral equations      see Applications to
Existence principle, for limit cycles      120 408
Existence principle, for nonrepelling fixed points      200
Existence principle, for periodic solutidns      see Periodic
Existence principle, for quasi-periodic solutions      see Applications to
Existence principle, for regular semi-linear operator equations      398
Existence principle, for saddle points      458
Existence principle, for systems of inequalities      61
Existence principle, for systems of real equations      53
Existence principle, Kronecker      520 529 569
Existence principle, Leray - Schauder      245 556 629 631
Existence principle, mapping degree and      569
Extension of compact operators      698
Extension of continuous operators      49 598 756
Extension of homotopies      698
Extension of Lipschitz-continuous operators      44
Exterior point      751
F-derivative, asymptotic      296

F-derivative, basic definition of      135
F-derivative, basic ideas of      131
F-derivative, compactness of      296
F-derivative, nth order      136
F-differential, basic definition of      135
F-differential, basic ideas of      131
F-differential, nth order      143
F-differential, symmetry of the      195
Factor space      765 770
Family of operators, equicontinuous      772 783
Family of operators, pointwise bounded      783
Feigenbaum bifurcation      738
Feigenbaum conjecture      738
Feigenbaum universality theory      723 738
Filter      800
Finite $\varepsilon$ -net      762
Finite-dimensional      765
fixed-point      9 447
Fixed-point index      529
Fixed-point index, additivity      529
Fixed-point index, algebraic topology and      see Part V
Fixed-point index, and analytic maps      613ff 621 625
Fixed-point index, and differentiable maps      613ff 619
Fixed-point index, and essential maps      693ff 710
Fixed-point index, and homeomorphisms      574ff 626 704ff
Fixed-point index, and iterated maps      724
Fixed-point index, at infinity      650
Fixed-point index, axioms (Aone)-(Afour) for the      529
Fixed-point index, basic applications      525
Fixed-point index, basic ideas      519
Fixed-point index, basic properties      529 530 574 615
Fixed-point index, basic theorems, Borsuk antipodal theorem      700
Fixed-point index, basic theorems, commutativity theorem      573 731
Fixed-point index, basic theorems, Cronin - Schwartz theorem for fixed-point index, basic theorems, analytic maps      621
Fixed-point index, basic theorems, existence and uniqueness in $\mathbb{R}^{N}$       535
Fixed-point index, basic theorems, existence and uniqueness in B-spaces      542
Fixed-point index, basic theorems, factorization theorem      579
Fixed-point index, basic theorems, Hopf classification theorem      711
Fixed-point index, basic theorems, index sum theorem      532
Fixed-point index, basic theorems, Krasnoselskii - Zabreiko - Steinlein fixed-point index, basic theorems, mod theorem      724
Fixed-point index, basic theorems, Leray - Schauder index theorem      619
Fixed-point index, basic theorems, Leray product theorem      575
Fixed-point index, basic theorems, product theorem      546
Fixed-point index, basic theorems, reduction theorem      547
Fixed-point index, basic theorems, relation principle      638 733
Fixed-point index, basic theorems, topological invariance of the fixed- point index      578
Fixed-point index, boundary dependence      530
Fixed-point index, commutativity      573 731
Fixed-point index, computing methods      616 619 621 637ff 650 688 732
Fixed-point index, computing methods, basic ideas      522 554 614ff
Fixed-point index, construction of the      537 542
Fixed-point index, continuity of the      531
Fixed-point index, differential topology and      663; see Parts IV and V
Fixed-point index, excision property      530
Fixed-point index, existence for special classes, of mappings      see Mapping degree
Fixed-point index, existence for special classes, of mappings, -compact maps      604
Fixed-point index, existence for special classes, of mappings, basic situation (compact maps)      542
Fixed-point index, existence for special classes, of mappings, classes, of mappings, continuous maps in $\mathbb{R}^{N}$       535
Fixed-point index, existence for special classes, of mappings, condensing maps      606
Fixed-point index, existence for special classes, of mappings, overview of generalizations in Parts II and V      600
Fixed-point index, existence on special spaces, basic situation (B-space)      542
Fixed-point index, existence on special spaces, closed convex sets      604
Fixed-point index, existence on special spaces, connected ANRs      608
Fixed-point index, existence on special spaces, euclidean neighborhood retracts (ENRs)      609
Fixed-point index, existence on special spaces, euclidean spaces      535
Fixed-point index, existence on special spaces, locally convex spaces      607
Fixed-point index, existence on special spaces, manifolds      see Part V
Fixed-point index, general proof strategy via approximation and general position      525 537 542
Fixed-point index, generalized homotopy invariance      572
Fixed-point index, homotopy invariance      529
Fixed-point index, local      532
Fixed-point index, relation between fixed-point index and mapping degree      531
Fixed-point index, uniqueness of solutions and      613 622 624 649
Fixed-point theorem, Altmann      556
Fixed-point theorem, Amann      304 506 512
Fixed-point theorem, Arnold - Conley - Zehnder      737
Fixed-point theorem, asymptotic      724 725
Fixed-point theorem, Atiyah - Bott      68
Fixed-Point Theorem, Banach      17
Fixed-point theorem, Begle      68; see Part V
Fixed-point theorem, Birkho      ff 65
Fixed-point theorem, Birkhoff - Lewis - Moser      737
Fixed-point theorem, Bohl      602
Fixed-point theorem, Bohnenlust - Karlin      452
Fixed-point theorem, Bourbaki - Kneser      504
Fixed-point theorem, Brouwer      51
Fixed-point theorem, Browder      200 454 725
Fixed-point theorem, Browder - G $\ddot{o}$ hde - Kirk      478
Fixed-point theorem, Darbo      500
Fixed-point theorem, Fan - Glicksberg      452
Fixed-point theorem, for asymptotic linear operators      297
Fixed-point theorem, for coercive mappings      603
Fixed-point theorem, for cone expansions      562
Fixed-point theorem, for contractive maps on compact sets      39
Fixed-point theorem, for diametric contractions      512
Fixed-point theorem, for multivalued mappings      449 452 454
Fixed-point theorem, for perturbed operators      501
Fixed-point theorem, for spheres      602
Fixed-point theorem, for uniform structures      65
Fixed-point theorem, generalized Banach      39 449 500 501 724 731
Fixed-point theorem, generalized Brouwer      509 609
Fixed-point theorem, generalized Schauder      452 500 501 556 624 725
Fixed-point theorem, Kakutani      452
Fixed-point theorem, Kirk      485
Fixed-point theorem, Krasnoselskii      501 562
Fixed-point theorem, Krasnoselskii - Perov      546
Fixed-point theorem, Lefschetz      609
Fixed-point theorem, Leray - Schauder      245 556
Fixed-point theorem, Markov - Kakutani      66
Fixed-point theorem, Moser      736
Fixed-point theorem, Muhamadiev - Pokorny      561
Fixed-point theorem, Nussbaum      200
Fixed-point theorem, on common fixed points      66 486
Fixed-point theorem, on infinitely many fixed points      563
Fixed-point theorem, on multiple fixed points      304 561
Fixed-point theorem, on three fixed points      304
Fixed-point theorem, on unique fixed points      17 39 624 649
Fixed-point theorem, Poincar $\acute{e}$ - Birkho      ff 65
Fixed-point theorem, Poincar $\acute{e}$ - Bohl      571
Fixed-point theorem, Reinermann      501
Fixed-point theorem, Rothe      556
Fixed-point theorem, Ryll - Nardzewski      486
Fixed-point theorem, Sadovskii      500
Fixed-point theorem, Schauder      56
Fixed-point theorem, Schauder (second fixed-point theorem)      452
Fixed-point theorem, Tarski      506
Fixed-point theorem, Tihonov      65 452
Fixed-point theorem, with acute angle condition      556
Fixed-point theorem, with boundary condition      454
Fixed-point theorem, with omitted ray condition      555
Fixed-point, classification, -stable      see Contracting
Fixed-point, classification, -unstable      160
Fixed-point, classification, -weakly stable      see Nonexpanding
Fixed-point, classification, attracting      158
Fixed-point, classification, center-like      160
Fixed-point, classification, contracting      160
Fixed-point, classification, ejective      158
Fixed-point, classification, hyperbolic      160
Fixed-point, classification, nonexpanding      160
Fixed-point, classification, regular      184
Fixed-point, classification, repelling      158
Fixed-point, classification, singular      184
Fixed-point, classification, stable in the strict sense      224
Fixed-point, classification, weakly regular      619
Fixed-point, common      66 486
Fixed-point, multiplicity of a      617
Fixed-point, property      65
Fixed-point, space      65 609
Fixed-point, trick for periodic solutions      86
Fixed-point, trick for quasi-linear equations      246

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