Introduction to functional differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1993
|
| Series: | Applied mathematical sciences
99 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [419] - 443 |
| Physical Description: | X, 447 S. graph. Darst. |
| ISBN: | 0387940766 3540940766 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to functional differential equations |c Jack K. Hale ; Sjoerd M. Verduyn Lunel |
| 264 | 1 | |a New York u.a. |b Springer |c 1993 | |
| 300 | |a X, 447 S. |b graph. Darst. | ||
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| 490 | 1 | |a Applied mathematical sciences |v 99 | |
| 500 | |a Literaturverz. S. [419] - 443 | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Introduction 1
1. Linear differential difference equations 11
1.1 Differential and difference equations 11
1.2 Retarded differential difference equations 13
1.3 Exponential estimates of x( j), /) 15
1.4 The characteristic equation 17
1.5 The fundamental solution 18
1.6 The variation of constants formula 23
1.7 Neutral differential difference equations 25
1.8 Supplementary remarks 34
2. Functional differential equations: Basic theory 38
2.1 Definition of a retarded equation 38
2.2 Existence, uniqueness, and continuous dependence 39
2.3 Continuation of solutions 44
2.4 Differentiability of solutions 48
2.5 Backward continuation 51
2.6 Caratheodory conditions 58
2.7 Definition of a neutral equation 59
2.8 Fundamental properties of NFDE 61
2.9 Supplementary remarks 65
3. Properties of the solution map 67
3.1 Finite or infinite dimensional problem? 68
3.2 Equivalence classes of solutions 70
3.3 Small solutions for linear equations 74
3.4 Unique backward extensions 86
3.5 Range in Mn 87
viii Contents
3.6 Compactness and representation 89
3.7 The solution map for NFDE 91
3.8 Supplementary remarks 97
4. Autonomous and periodic processes 100
4.1 Processes 100
4.2 Invariance 104
4.3 Discrete systems—Maximal invariant sets and attractors 107
4.4 Fixed points of discrete dissipative processes 115
4.5 Continuous systems—Maximal invariant sets and attractors .... 119
4.6 Stability and maximal invariant sets in processes 121
4.7 Convergent systems 125
4.8 Supplementary remarks 127
5. Stability theory 130
5.1 Definitions 130
5.2 The method of Liapunov functionals 132
5.3 Liapunov functionals for autonomous systems 143
5.4 Razumikhin theorems 151
5.5 Supplementary remarks 161
6. General linear systems 167
6.1 Resolvents and exponential estimates 167
6.2 The variation of constants formula 173
6.3 The formal adjoint equation 176
6.4 Boundary value problems 180
6.5 Stability and boundedness 184
6.6 Supplementary remarks 186
7. Linear autonomous equations 193
7.1 Strongly continuous semigroups 193
7.2 Spectrum of the generator—Decomposition of C 197
7.3 Characteristic matrices and equivalence 200
7.4 The generalized eigenspace for RFDE 205
7.5 Decomposing C with the adjoint equation 208
7.6 Estimates on the complementary subspace 213
7.7 An example 215
7.8 Spectral decomposition according to all eigenvalues 218
7.9 The decomposition in the variation of constants formula 225
7.10 Parameter dependence 230
7.11 Supplementary remarks 232
Contents ix
8. Periodic systems 236
8.1 General theory 236
8.2 Decomposition 241
8.3 An example: Integer delays 247
8.4 Supplementary remarks 254
9. Equations of neutral type 255
9.1 General linear systems 255
9.2 Linear autonomous equations 262
9.3 Exponential estimates 269
9.4 Hyperbolic semigroups 275
9.5 Variation of constants formula 279
9.6 Strongly stable D operators 284
9.7 Properties of equations with stable D operators 290
9.8 Stability theory 292
9.9 Supplementary remarks 296
10. Near equilibrium and periodic orbits 302
10.1 Hyperbolic equilibrium points 302
10.2 Nonhyperbolic equilibrium points 312
10.3 Hyperbolic periodic orbits 317
10.4 Nondegenerate periodic orbits of RFDE 324
10.5 Supplementary remarks 329
11. Periodic solutions of autonomous equations 331
11.1 Hopf bifurcation 331
11.2 A periodicity theorem 335
11.3 Range of the period 338
11.4 The equation x(t) = ax(t 1)[1 + x{t) 341
11.5 The equation x(t) = ax{t 1)[1 x2{t) 347
11.6 The equation x(t) + f(x(t))x(t) + g{x{t r)) = 0 348
11.7 Supplementary remarks 355
12. Additional topics 364
12.1 Equations on manifolds—Definitions and examples 364
12.2 Dimension of the global attractor 369
12.3 ^ stability and Morse Smale maps 372
12.4 Hyperbolicity is generic 376
12.5 One to oneness on the attractor 379
12.6 Morse decompositions 382
12.7 Singularly perturbed systems 386
12.8 Averaging 396
x Contents
12.9 Infinite delay 401
12.10 Supplementary remarks 406
Appendix: Stability of characteristic equations 414
Bibliography 419
Index 444
List of Symbols 447
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:25:31Z |
| institution | BVB |
| isbn | 0387940766 3540940766 |
| language | English |
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| physical | X, 447 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Hale, Jack K. 1928-2009 Verfasser (DE-588)172122503 aut Introduction to functional differential equations Jack K. Hale ; Sjoerd M. Verduyn Lunel New York u.a. Springer 1993 X, 447 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 99 Literaturverz. S. [419] - 443 Functional differential equations Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf Funktional-Differentialgleichung (DE-588)4155668-9 s DE-604 Verduyn Lunel, Sjoerd M. Verfasser aut Applied mathematical sciences 99 (DE-604)BV000005274 99 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005833422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hale, Jack K. 1928-2009 Verduyn Lunel, Sjoerd M. Introduction to functional differential equations Applied mathematical sciences Functional differential equations Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| subject_GND | (DE-588)4155668-9 |
| title | Introduction to functional differential equations |
| title_auth | Introduction to functional differential equations |
| title_exact_search | Introduction to functional differential equations |
| title_full | Introduction to functional differential equations Jack K. Hale ; Sjoerd M. Verduyn Lunel |
| title_fullStr | Introduction to functional differential equations Jack K. Hale ; Sjoerd M. Verduyn Lunel |
| title_full_unstemmed | Introduction to functional differential equations Jack K. Hale ; Sjoerd M. Verduyn Lunel |
| title_short | Introduction to functional differential equations |
| title_sort | introduction to functional differential equations |
| topic | Functional differential equations Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| topic_facet | Functional differential equations Funktional-Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005833422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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