Theory of differential equations with unbounded delay:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1994
|
| Series: | Mathematics and its applications
298 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 385 S. |
| ISBN: | 079233003X |
Staff View
MARC
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| 245 | 1 | 0 | |a Theory of differential equations with unbounded delay |c by V. Lakshmikantham ; Lizhi Wen and Binggen Zhang |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1994 | |
| 300 | |a XI, 385 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 298 | |
| 650 | 4 | |a Equation Volterra | |
| 650 | 4 | |a Oscillation | |
| 650 | 4 | |a Solution périodique | |
| 650 | 4 | |a Stabilité | |
| 650 | 4 | |a Théorème Nussbaum | |
| 650 | 4 | |a Théorème Razumikhin | |
| 650 | 7 | |a Équations différentielles à retard - Congrès |2 ram | |
| 650 | 4 | |a Delay differential equations | |
| 650 | 0 | 7 | |a Differentialgleichung mit nacheilendem Argument |0 (DE-588)4199298-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung mit nacheilendem Argument |0 (DE-588)4199298-2 |D s |
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| 700 | 1 | |a Wen, Lizhi |e Verfasser |4 aut | |
| 700 | 1 | |a Zhang, Binggen G. |e Verfasser |4 aut | |
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Record in the Search Index
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CONTENTS
PREFACE ix
CHAPTER 1. PRELIMINARIES 1
1.0 Introduction 1
1.1 Classification and Description 2
1.2 Notes and Comments 13
CHAPTER 2. EXISTENCE THEORY FOR p TYPE NFDE 15
2.0 Introduction 15
2.1 Existence and Uniqueness 15
2.2 Continuous Dependence 33
2.3 Differentiability Relative to Initial Data 38
2.4 Continuation of Solutions 41
2.5 Notes and Comments 45
CHAPTER 3. EXISTENCE THEORY OF NFDE WITH
INFINITE DELAY 47
3.0 Introduction 47
3.1 Description of Phase Spaces 48
3.2 Existence and Uniqueness 50
3.3 Continuation of Solutions 56
3.4 Implication to Admissible Phase Spaces 61
3.5 Notes and Comments 72
vi Theory of Differential Equations with Unbounded Delay
CHAPTER 4. STABILITY AND BOUNDEDNESS FOR RFDE WITH
BOUNDED DELAY 75
4.0 Introduction 75
4.1 Definitions 76
4.2 Classical Results for Stability 79
4.3 Razumikhin type Theorems with Lyapunov Functionals 82
4.4 Stability in Terms of Two Measures 101
4.5 Weak Exponential Asymptotical Stability Ill
4.6 Boundedness Criteria 123
4.7 Notes and Comments 125
CHAPTER 5. STABILITY CRITERIA FOR p TYPE NFDE 127
5.0 Introduction 127
5.1 Stability Criteria 127
5.2 Boundedness Results ^ 149
5.3 Notes and Comments 174
CHAPTER 6. STABILITY AND BOUNDEDNESS FOR EQUATIONS
WITH INFINITE DELAY 177
6.0 Introduction 177
6.1 Notation and Definitions 177
6.2 Stability in Terms of Two Measures 180
6.3 Boundedness in Terms of Two Measures 194
6.4 Razumikhin's Method for NFDE by Comparison Method . 211
6.5 Notes and Comments 243
CHAPTER 7. ASYMPTOTIC BEHAVIOR 245
7.0 Introduction 245
7.1 Invariance Principle 245
7.2 Convergence of Solutions 257
7.3 Asymptotic Behavior 268
7.4 Notes and Comments 273
CHAPTER 8. OSCILLATION THEORY 275
8.0 Introduction 275
8.1 Oscillation of Systems 275
8.2 Oscillation of Scalar Equations 283
8.3 Comparison Theorems 289
8.4 Nonoscillatory Solutions 296
8.5 Notes and Comments 304
Contents vii
CHAPTER 9. PERIODIC SOLUTIONS 307
9.0 Introduction 307
9.1 Extension of ODE Methods 308
9.2 Periodic Solutions Generated by ODEs 317
9.3 Nussbaum's Fixed Point Theorem 328
9.4 Periodic Delay Logistic Equations 332
9.5 Volterra Equations with Infinite Delay 341
9.6 Method of Lyapunov Functionals 349
9.7 Notes and Comments 354
REFERENCES 355
INDEX 383 |
| any_adam_object | 1 |
| author | Lakshmikantham, Vangipuram 1926-2012 Wen, Lizhi Zhang, Binggen G. |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009795435 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T09:01:11Z |
| institution | BVB |
| isbn | 079233003X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006480249 |
| oclc_num | 30733939 |
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| owner | DE-12 DE-703 DE-11 DE-188 |
| owner_facet | DE-12 DE-703 DE-11 DE-188 |
| physical | XI, 385 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Lakshmikantham, Vangipuram 1926-2012 Verfasser (DE-588)104268050 aut Theory of differential equations with unbounded delay by V. Lakshmikantham ; Lizhi Wen and Binggen Zhang Dordrecht u.a. Kluwer 1994 XI, 385 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 298 Equation Volterra Oscillation Solution périodique Stabilité Théorème Nussbaum Théorème Razumikhin Équations différentielles à retard - Congrès ram Delay differential equations Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 s DE-604 Wen, Lizhi Verfasser aut Zhang, Binggen G. Verfasser aut Mathematics and its applications 298 (DE-604)BV008163334 298 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006480249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926-2012 Wen, Lizhi Zhang, Binggen G. Theory of differential equations with unbounded delay Mathematics and its applications Equation Volterra Oscillation Solution périodique Stabilité Théorème Nussbaum Théorème Razumikhin Équations différentielles à retard - Congrès ram Delay differential equations Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd |
| subject_GND | (DE-588)4199298-2 |
| title | Theory of differential equations with unbounded delay |
| title_auth | Theory of differential equations with unbounded delay |
| title_exact_search | Theory of differential equations with unbounded delay |
| title_full | Theory of differential equations with unbounded delay by V. Lakshmikantham ; Lizhi Wen and Binggen Zhang |
| title_fullStr | Theory of differential equations with unbounded delay by V. Lakshmikantham ; Lizhi Wen and Binggen Zhang |
| title_full_unstemmed | Theory of differential equations with unbounded delay by V. Lakshmikantham ; Lizhi Wen and Binggen Zhang |
| title_short | Theory of differential equations with unbounded delay |
| title_sort | theory of differential equations with unbounded delay |
| topic | Equation Volterra Oscillation Solution périodique Stabilité Théorème Nussbaum Théorème Razumikhin Équations différentielles à retard - Congrès ram Delay differential equations Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd |
| topic_facet | Equation Volterra Oscillation Solution périodique Stabilité Théorème Nussbaum Théorème Razumikhin Équations différentielles à retard - Congrès Delay differential equations Differentialgleichung mit nacheilendem Argument |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006480249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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