Basic theory of ordinary differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
1999
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seiten 453 - 461 |
| Beschreibung: | XI, 468 Seiten graph. Darst. |
| ISBN: | 0387986995 |
Internformat
MARC
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| 245 | 1 | 0 | |a Basic theory of ordinary differential equations |c Po-Fang Hsieh, Yasutaka Sibuya |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 1999 | |
| 300 | |a XI, 468 Seiten |b graph. Darst. | ||
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| 650 | 4 | |a Gewöhnliche Differentialgleichung - Lehrbuch | |
| 650 | 4 | |a Differential equations | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface vii
Chapter I. Fundamental Theorems of Ordinary Differential Equations 1
1 1. Existence and uniqueness with the Lipschitz condition 1
1 2. Existence without the Lipschitz condition 8
1 3. Some global properties of solutions 15
1 4. Analytic differential equations 20
Exercises I 23
Chapter II. Dependence on Data 28
II 1. Continuity with respect to initial data and parameters 28
II 2. Differentiability 32
Exercises II 35
Chapter III. Nonuniqueness 41
III l. Examples 41
III 2. The Kneser theorem 45
III 3. Solution curves on the boundary of Tl(A) 49
III 4. Maximal and minimal solutions 52
III 5. A comparison theorem 58
III 6. Sufficient conditions for uniqueness 61
Exercises III 66
Chapter IV. General Theory of Linear Systems 69
IV 1. Some basic results concerning matrices 69
IV 2. Homogeneous systems of linear differential equations 78
IV 3. Homogeneous systems with constant coefficients 81
IV 4. Systems with periodic coefficients 87
IV 5. Linear Hamiltonian systems with periodic coefficients 90
IV 6. Nonhomogeneous equations 96
IV 7. Higher order scalar equations 98
Exercises IV 102
Chapter V. Singularities of the First Kind 108
V l. Formal solutions of an algebraic differential equation 109
V 2. Convergence of formal solutions of a system of the first kind 113
V 3. The S N decomposition of a matrix of infinite order 118
V 4. The S N decomposition of a differential operator 120
V 5. A normal form of a differential operator 121
V 6. Calculation of the normal form of a differential operator 130
V 7. Classification of singularities of homogeneous linear systems 132
Exercises V 137
ix
x CONTENTS
Chapter VI. Boundary Value Problems of Linear Differential
Equations of the Second Order 144
VI 1. Zeros of solutions 144
VI 2. Sturm Liouville problems 148
VI 3. Eigenvalue problems 153
VI 4. Eigenfunction expansions 162
VI 5. Jost solutions 168
VI 6. Scattering data 172
VI 7. Reflectionless potentials 175
VI 8. Construction of a potential for given data 178
VI 9. Differential equations satisfied by reflectionless potentials 181
VI 10. Periodic potentials 183
Exercises VI 190
Chapter VII. Asymptotic Behavior of Solutions of Linear Systems 197
VII 1. Liapounoff s type numbers 197
VII 2. Liapounoff s type numbers of a homogeneous linear system 199
VII 3. Calculation of Liapounoff s type numbers of solutions 203
VII 4. A diagonalization theorem 212
VII 5. Systems with asymptotically constant coefficients 219
VII 6. An application of the Floquet theorem 225
Exercises VII 230
Chapter VIII. Stability 235
VIII 1. Basic definitions 235
VIII 2. A sufficient condition for asymptotic stability 241
VIII 3. Stable manifolds 243
VIII 4. Analytic structure of stable manifolds 246
VIII 5. Two dimensional linear systems with constant coefficients 251
VIII 6. Analytic systems in M2 255
VIII 7. Perturbations of an improper node and a saddle point 261
VIII 8. Perturbations of a proper node 266
VIII 9. Perturbation of a spiral point 270
VIII 10. Perturbation of a center 271
Exercises VIII 274
Chapter IX. Autonomous Systems 279
LX 1. Limit invariant sets 279
IX 2. Liapounoff s direct method 281
IX 3. Orbital stability 283
IX 4. The Poincare Bendixson theorem 291
IX 5. Indices of Jordan curves 293
Exercises IX 298
CONTENTS xi
Chapter X. The Second Order Differential Equation
d x der
w + h{x) +g{x)=0 304
X l. Two point boundary value problems 305
X 2. Applications of the Liapounoff functions 309
X 3. Existence and uniqueness of periodic orbits 313
X 4. Multipliers of the periodic orbit of the van der Pol equation 318
X 5. The van der Pol equation for a small e 0 319
X 6. The van der Pol equation for a large parameter 322
X 7. A theorem due to M. Nagumo 327
X 8. A singular perturbation problem 330
Exercises X 334
Chapter XI. Asymptotic Expansions 342
XI 1. Asymptotic expansions in the sense of Poincare 342
XI 2. Gevrey asymptotics 353
XI 3. Flat functions in the Gevrey asymptotics 357
XI 4. Basic properties of Gevrey asymptotic expansions 360
XI 5. Proof of Lemma XI 2 6 363
Exercises XI 365
Chapter XII. Asymptotic Expansions in a Parameter 372
XII 1. An existence theorem 372
XII 2. Basic estimates 374
XII 3. Proof of Theorem XII 1 2 378
XII 4. A block diagonalization theorem 380
XII 5. Gevrey asymptotic solutions in a parameter 385
XII 6. Analytic simplification in a parameter 390
Exercises XII 395
Chapter XIII. Singularities of the Second Kind 403
XIII 1. An existence theorem 403
XIII 2. Basic estimates 406
XIII 3. Proof of Theorem XIII 1 2 417
XIII 4. A block diagonalization theorem 420
XIII 5. Cyclic vectors (A lemma of P. Deligne) 424
XIII 6. The Hukuhara Turrittin theorem 428
XIII 7. An n th order linear differential equation at a singular point
of the second kind 436
XIII 8. Gevrey property of asymptotic solutions at an irregular
singular point 441
Exercises XIII 443
References 453
Index 462
|
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| institution | BVB |
| isbn | 0387986995 |
| language | English |
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| physical | XI, 468 Seiten graph. Darst. |
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| series2 | Universitext |
| spelling | Hsieh, Po-Fang Verfasser aut Basic theory of ordinary differential equations Po-Fang Hsieh, Yasutaka Sibuya New York, NY [u.a.] Springer 1999 XI, 468 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverzeichnis Seiten 453 - 461 Gewöhnliche Differentialgleichung - Lehrbuch Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Shibuya, Yasutaka 1930- Verfasser (DE-588)121295656 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008694038&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsieh, Po-Fang Shibuya, Yasutaka 1930- Basic theory of ordinary differential equations Gewöhnliche Differentialgleichung - Lehrbuch Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4123623-3 |
| title | Basic theory of ordinary differential equations |
| title_auth | Basic theory of ordinary differential equations |
| title_exact_search | Basic theory of ordinary differential equations |
| title_full | Basic theory of ordinary differential equations Po-Fang Hsieh, Yasutaka Sibuya |
| title_fullStr | Basic theory of ordinary differential equations Po-Fang Hsieh, Yasutaka Sibuya |
| title_full_unstemmed | Basic theory of ordinary differential equations Po-Fang Hsieh, Yasutaka Sibuya |
| title_short | Basic theory of ordinary differential equations |
| title_sort | basic theory of ordinary differential equations |
| topic | Gewöhnliche Differentialgleichung - Lehrbuch Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Gewöhnliche Differentialgleichung - Lehrbuch Differential equations Gewöhnliche Differentialgleichung Lehrbuch |
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