Uniqueness and nonuniqueness criteria for ordinary differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1993
|
| Series: | Series in real analysis
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 312 S. |
| ISBN: | 9810213573 |
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MARC
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| 245 | 1 | 0 | |a Uniqueness and nonuniqueness criteria for ordinary differential equations |c R. P. Agarwal ; V. Lakshmikantham |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1993 | |
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Record in the Search Index
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| adam_text |
CONTENTS
Preface
CHAPTER 1
FIRST ORDER DIFFERENTIAL EQUATIONS
1.1 Introduction 1
1.2 Lipschitz uniqueness theorem 2
1.3 Peano's uniqueness theorem 10
1.4 Osgood's uniqueness theorem 12
1.5 Montel Tonelli's uniqueness theorem 19
1.6 Nagumo's uniqueness theorem 19
1.7 Krasnosel'skii Krein's uniqueness theorem 26
1.8 Kooi's uniqueness theorem 30
1.9 Roger's uniqueness theorem 33
1.10 Witte's uniqueness theorem 37
1.11 Perron's uniqueness theorem 41
1.12 Gyori's uniqueness theorem 43
1.13 Iyanaga's uniqueness theorem 51
1.14 Inaba's uniqueness theorem 53
1.15 Kamke's uniqueness theorem 56
1.16 Shen's uniqueness theorem 63
1.17 Mikolaj ska's uniqueness theorem 66
1.18 Brauer's uniqueness theorem 74
1.19 Wend's uniqueness theorem 77
1.20 van Kampen's uniqueness theorem 78
1.21 Yosie's uniqueness theorem 81
1.22 Kitagawa's uniqueness theorem 92
1.23 Tamarkine's nonuniqueness theorem 98
1.24 Lakshmikantham's nonuniqueness theorem 99
1.25 Samimi's nonuniqueness theorem 101
vii
viii CONTENTS
CHAPTER 2
FIRST ORDER DIFFERENTIAL EQUATIONS (CONTD.)
2.1 Introduction 102
2.2 Lipschitz uniqueness theorem 103
2.3 Nagumo's uniqueness theorem 106
2.4 Krasnosel'skii Krein's uniqueness theorem 106
2.5 Boruvka's uniqueness theorem 109
2.6 Wend's uniqueness theorem 110
2.7 Zabreiko's uniqueness theorem 113
2.8 Lakshmikantham's uniqueness theorem 119
2.9 Bownds' uniqueness theorem 121
2.10 Bownds Metcalf's uniqueness theorem 125
2.11 Gard's uniqueness theorem 127
2.12 Majorana's nonuniqueness theorem 130
CHAPTER 3
FIRST ORDER DIFFERENTIAL SYSTEMS
3.1 Introduction 134
3.2 Lipschitz uniqueness theorem 136
3.3 Peano's uniqueness theorem 139
3.4 Heins' uniqueness theorem 140
3.5 Giuliano's uniqueness theorem 143
3.6 Nagumo's uniqueness theorem 143
3.7 Witte's uniqueness theorem 144
3.8 Kamke's uniqueness theorem 144
3.9 Wend's uniqueness theorem 145
3.10 Bownds' uniqueness theorem 146
3.11 Gard's uniqueness theorem 150
3.12 Driver Norris' uniqueness theorem 151
3.13 Goebel Zur's uniqueness theorem 154
3.14 Bownds Diaz's uniqueness theorem 157
3.15 Okamura's uniqueness theorem 159
3.16 Chu Diaz's uniqueness theorem 167
3.17 Sato's uniqueness theorem 168
3.18 Brauer Steinberg's uniqueness theorem 172
3.19 Moyer's uniqueness theorem 174
3.20 Bernfeld Driver Lakshmikantham's uniqueness theorem 179
CONTENTS ix
3.21 Kaper Kwong's uniqueness theorem 183
3.22 Tesarova Dosly's uniqueness theorem 187
3.23 Antosiewicz's uniqueness theorem 191
3.24 Lakshmikantham Samimi's uniqueness theorem 193
3.25 Kalas' nonuniqueness theorem 197
3.26 Samimi's nonuniqueness theorem 201
CHAPTER 4
HIGHER ORDER DIFFERENTIAL EQUATIONS
4.1 Introduction 204
4.2 Lipschitz uniqueness theorem 206
4.3 Merli's uniqueness theorem 209
4.4 Kikodze's uniqueness theorem 211
4.5 Wend's uniqueness theorem 216
4.6 Redheffer's uniqueness theorem 219
4.7 Heidel's uniqueness theorem 222
CHAPTER 5
DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES
5.1 Introduction 225
5.2 Aziz Diaz's uniqueness theorem 227
5.3 Medeiros' uniqueness theorem 229
5.4 Diaz Weinacht's uniqueness theorem 231
5.5 Perron's uniqueness theorem 235
5.6 Olech's uniqueness theorem 235
5.7 Goldstein's uniqueness theorem 235
5.8 Arrate's uniqueness theorem 237
5.9 Ramankutty's uniqueness theorem 240
5.10 Murakami's uniqueness theorem 243
5.11 Lakshmikantham's uniqueness theorem 246
CHAPTER 6
COMPLEX DIFFERENTIAL EQUATIONS
6.1 Introduction 248
6.2 Deo Lakshmikantham's uniqueness theorem 249
x CONTENTS
CHAPTER 7
FUNCTIONAL DIFFERENTIAL EQUATIONS
7.1 Introduction 251
7.2 Lakshmikantham's uniqueness theorem 252
7.3 Lakshmikantham Leela's uniqueness theorem 254
7.4 Lakshmikantham Shendge's uniqueness theorem 254
7.5 Furumochi's uniqueness theorem 255
CHAPTER 8
IMPULSIVE DIFFERENTIAL EQUATIONS
8.1 Introduction 263
8.2 Hu Lakshmikantham's uniqueness theorem 265
8.3 Pandit's uniqueness theorem 266
CHAPTER 9
DIFFERENTIAL EQUATIONS WITH HYSTERESIS
9.1 Introduction 272
9.2 Borzdyko's uniqueness theorem 1 273
9.3 Borzdyko's uniqueness theorem 2 275
9.4 Borzdyko's uniqueness theorem 3 277
9.5 Borzdyko's uniqueness theorem 4 280
CHAPTER 10
GENERALIZED DIFFERENTIAL EQUATIONS
10.1 Introduction 282
10.2 Schwabik's uniqueness theorem 286
NOTES 295
REFERENCES 300 |
| any_adam_object | 1 |
| author | Agarwal, Ravi P. 1947- Lakshmikantham, Vangipuram 1926-2012 |
| author_GND | (DE-588)112040187 (DE-588)104268050 |
| author_facet | Agarwal, Ravi P. 1947- Lakshmikantham, Vangipuram 1926-2012 |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012738505 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T09:01:12Z |
| institution | BVB |
| isbn | 9810213573 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008661933 |
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| owner_facet | DE-703 DE-11 |
| physical | X, 312 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in real analysis |
| series2 | Series in real analysis |
| spelling | Agarwal, Ravi P. 1947- Verfasser (DE-588)112040187 aut Uniqueness and nonuniqueness criteria for ordinary differential equations R. P. Agarwal ; V. Lakshmikantham Singapore [u.a.] World Scientific 1993 X, 312 S. txt rdacontent n rdamedia nc rdacarrier Series in real analysis 6 Équations différentielles ram Differential equations Eindeutigkeit (DE-588)4151249-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Eindeutigkeit (DE-588)4151249-2 s DE-604 Lakshmikantham, Vangipuram 1926-2012 Verfasser (DE-588)104268050 aut Series in real analysis 6 (DE-604)BV001898092 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008661933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Agarwal, Ravi P. 1947- Lakshmikantham, Vangipuram 1926-2012 Uniqueness and nonuniqueness criteria for ordinary differential equations Series in real analysis Équations différentielles ram Differential equations Eindeutigkeit (DE-588)4151249-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4151249-2 (DE-588)4020929-5 |
| title | Uniqueness and nonuniqueness criteria for ordinary differential equations |
| title_auth | Uniqueness and nonuniqueness criteria for ordinary differential equations |
| title_exact_search | Uniqueness and nonuniqueness criteria for ordinary differential equations |
| title_full | Uniqueness and nonuniqueness criteria for ordinary differential equations R. P. Agarwal ; V. Lakshmikantham |
| title_fullStr | Uniqueness and nonuniqueness criteria for ordinary differential equations R. P. Agarwal ; V. Lakshmikantham |
| title_full_unstemmed | Uniqueness and nonuniqueness criteria for ordinary differential equations R. P. Agarwal ; V. Lakshmikantham |
| title_short | Uniqueness and nonuniqueness criteria for ordinary differential equations |
| title_sort | uniqueness and nonuniqueness criteria for ordinary differential equations |
| topic | Équations différentielles ram Differential equations Eindeutigkeit (DE-588)4151249-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Équations différentielles Differential equations Eindeutigkeit Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008661933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001898092 |
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