The theory of differential equations: classical and qualitative
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2010
|
| Edition: | Second edition |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 423 Seiten graph. Darst. |
| ISBN: | 9781441957825 |
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MARC
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Record in the Search Index
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Titel: The theory of differential equations
Autor: Kelley, Walter G.
Jahr: 2010
Contents
Preface ix
Chapter 1 First-Order Differential Equations 1
1.1 Basic Results 1
1.2 First-Order Linear Equations 4
1.3 Autonomous Equations 5
1.4 Generalized Logistic Equation 10
1.5 Bifurcation 14
1.6 Exercises 16
Chapter 2 Linear Systems 23
2.1 Introduction 23
2.2 The Vector Equation x' = A{t)x 27
2.3 The Matrix Exponential Function 42
2.4 Induced Matrix Norm 59
2.5 Floquet Theory 64
2.6 Exercises 76
Chapter 3 Autonomous Systems 87
3.1 Introduction 87
3.2 Phase Plane Diagrams 90
3.3 Phase Plane Diagrams for Linear Systems 96
3.4 Stability of Nonlinear Systems 107
3.5 Linearization of Nonlinear Systems 113
3.6 Existence and Nonexistence of Periodic
Solutions 120
3.7 Three-Dimensional Systems 134
3.8 Differential Equations and Mathematica 145
3.9 Exercises 149
Chapter 4 Perturbation Methods 161
4.1 Introduction 161
4.2 Periodic Solutions 172
4.3 Singular Perturbations 178
4.4 Exercises 186
Chapter 5 The Self-Adjoint Second-Order Differential
Equation 192
5.1 Basic Definitions 192
vii
viii Contents
5.2 An Interesting Example 197
5.3 Cauchy Function and Variation of
Constants Formula 1"
5.4 Sturm-Liouville Problems 204
5.5 Zeros of Solutions and Disconjugacy 212
5.6 Factorizations and Recessive and
Dominant Solutions 219
5.7 The Riccati Equation 229
5.8 Calculus of Variations 240
5.9 Green's Functions 251
5.10 Exercises 272
Chapter 6 Linear Differential Equations of Order n 281
6.1 Basic Results 281
6.2 Variation of Constants Formula 283
6.3 Green's Functions 287
6.4 Factorizations and Principal Solutions 297
6.5 Adjoint Equation 302
6.6 Exercises 307
Chapter 7 BVPs for Nonlinear Second-Order DEs 309
7.1 Contraction Mapping Theorem (CMT) 309
7.2 Application of the CMT to a Forced
Equation 311
7.3 Applications of the CMT to BVPs 313
7.4 Lower and Upper Solutions 325
7.5 Nagumo Condition 334
7.6 Exercises 340
Chapter 8 Existence and Uniqueness Theorems 345
8.1 Basic Results 345
8.2 Lipschitz Condition and Picard-Lindelof
Theorem 348
8.3 Equicontinuity and the Ascoli-Arzela
Theorem 356
8.4 Cauchy-Peano Theorem 358
8.5 Extendability of Solutions 363
8.6 Basic Convergence Theorem 369
8.7 Continuity of Solutions with Respect to ICs 372
8.8 Kneser's Theorem 375
8.9 Differentiating Solutions with Respect to ICs 378
8.10 Maximum and Minimum Solutions 387
8.11 Exercises 396
Solutions to Selected Problems 403
Bibliography 415
Index 419 |
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| spelling | Kelley, Walter G. Verfasser aut The theory of differential equations classical and qualitative Walter G. Kelley, Allan C. Peterson Second edition New York, NY [u.a.] Springer 2010 XI, 423 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Differentialgleichung (DE-588)4012249-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgleichung (DE-588)4012249-9 s DE-604 Peterson, Allan C. 1942- Verfasser (DE-588)1088765971 aut Erscheint auch als Online-Ausgabe 978-1-4419-5783-2 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3430869&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020198957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kelley, Walter G. Peterson, Allan C. 1942- The theory of differential equations classical and qualitative Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4123623-3 |
| title | The theory of differential equations classical and qualitative |
| title_auth | The theory of differential equations classical and qualitative |
| title_exact_search | The theory of differential equations classical and qualitative |
| title_full | The theory of differential equations classical and qualitative Walter G. Kelley, Allan C. Peterson |
| title_fullStr | The theory of differential equations classical and qualitative Walter G. Kelley, Allan C. Peterson |
| title_full_unstemmed | The theory of differential equations classical and qualitative Walter G. Kelley, Allan C. Peterson |
| title_short | The theory of differential equations |
| title_sort | the theory of differential equations classical and qualitative |
| title_sub | classical and qualitative |
| topic | Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentialgleichung Lehrbuch |
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