Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations

Cover......Page 1
Title page......Page 2
Preface......Page 4
1.1 Introduction......Page 12
1.2 Lipschitz uniqueness theorem......Page 13
1.3 Peano's uniqueness theorem......Page 21
1.4 Osgood's uniqueness theorem......Page 23
1.6 Nagumo's uniqueness theorem......Page 30
1.7 Krasnosel'skii-Krein's uniqueness theorem......Page 37
1.8 Kooi's uniqueness theorem......Page 41
1.9 Roger's uniqueness theorem......Page 44
1.10 Witte's uniqueness theorem......Page 48
1.11 Perron's uniqueness theorem......Page 52
1.12 Gyori's uniqueness theorem......Page 54
1.13 Iyanaga's uniqueness theorem......Page 62
1.14 Inaba's uniqueness theorem......Page 64
1.15 Kamke's uniqueness theorem......Page 67
1.16 Shen's uniqueness theorem......Page 74
1.17 Mikolajska's uniqueness theorem......Page 77
1.18 Brauer's uniqueness theorem......Page 85
1.19 Wend's uniqueness theorem......Page 88
1.20 van Kampen's uniqueness theorem......Page 89
1.21 Yosie's uniqueness theorem......Page 92
1.22 Kitagawa's uniqueness theorem......Page 103
1.23 Tamarkine's nonuniqueness theorem......Page 109
1.24 Lakshmikantham's nonuniqueness theorem......Page 110
1.25 Samimi's nonuniqueness theorem......Page 112
2.1 Introduction......Page 113
2.2 Lipschitz uniqueness theorem......Page 114
2.4 Krasnosel'skii-Krein's uniqueness theorem......Page 117
2.5 Borùvka's uniqueness theorem......Page 120
2.6 Wend's uniqueness theorem......Page 121
2.7 Zabreiko's uniqueness theorem......Page 124
2.8 Lakshmikantham's uniqueness theorem......Page 130
2.9 Bownds' uniqueness theorem......Page 132
2.10 Bownds-Metcalf's uniqueness theorem......Page 136
2.11 Gard's uniqueness theorem......Page 138
2.12 Majorana's nonuniqueness theorem......Page 141
3.1 Introduction......Page 145
3.2 Lipschitz uniqueness theorem......Page 147
3.3 Peano's uniqueness theorem......Page 150
3.4 Heins' uniqueness theorem......Page 151
3.6 Nagumo's uniqueness theorem......Page 154
3.8 Kamke's uniqueness theorem......Page 155
3.9 Wend's uniqueness theorem......Page 156
3.10 Bownds' uniqueness theorem......Page 157
3.11 Gard's uniqueness theorem......Page 161
3.12 Driver-Norris' uniqueness theorem......Page 162
3.13 Goebel-Zur's uniqueness theorem......Page 165
3.14 Bownds-Diaz's uniqueness theorem......Page 168
3.15 Okamura's uniqueness theorem......Page 170
3.16 Chu-Diaz's uniqueness theorem......Page 178
3.17 Sato's uniqueness theorem......Page 179
3.18 Brauer-Sternberg's uniqueness theorem......Page 183
3.19 Moyer's uniqueness theorem......Page 185
3.20 Bernfeld-Driver-Lakshmikantham's uniqueness theorem......Page 190
3.21 Kaper-Kwong's uniqueness theorem......Page 194
3.22 Tesarova-Dosly's uniqueness theorem......Page 198
3.23 Antosiewicz's uniqueness theorem......Page 202
3.24 Lakshmikantham-Samimi's uniqueness theorem......Page 204
3.25 Kalas' nonuniqueness theorem......Page 208
3.26 Samimi's nonuniqueness theorem......Page 212
4.1 Introduction......Page 215
4.2 Lipschitz uniqueness theorem......Page 217
4.3 Merli's uniqueness theorem......Page 220
4.4 Kikodze's uniqueness theorem......Page 222
4.5 Wend's uniqueness theorem......Page 227
4.6 Redheffer's uniqueness theorem......Page 230
4.7 Heidel's uniqueness theorem......Page 233
5.1 Introduction......Page 236
5.2 Aziz-Diaz's uniqueness theorem......Page 238
5.3 Medeiros' uniqueness theorem......Page 240
5.4 Diaz-Weinacht's uniqueness theorem......Page 242
5.7 Goldstein's uniqueness theorem......Page 246
5.8 Arrate's uniqueness theorem......Page 248
5.9 Ramankutty's uniqueness theorem......Page 251
5.10 Murakami's uniqueness theorem......Page 254
5.11 Lakshmikantham's uniqueness theorem......Page 257
6.1 Introduction......Page 259
6.2 Deo-Lakshmikantham's uniqueness theorem......Page 260
7.1 Introduction......Page 262
7.2 Lakshmikantham's uniqueness theorem......Page 263
7.4 Lakshmikantham-Shendge's uniqueness theorem......Page 265
7.5 Furumochi's uniqueness theorem......Page 266
8.1 Introduction......Page 274
8.2 Hu-Lakshmikantham's uniqueness theorem......Page 276
8.3 Pandit's uniqueness theorem......Page 277
9.1 Introduction......Page 283
9.2 Borzdyko's uniqueness theorem 1......Page 284
9.3 Borzdyko's uniqueness theorem 2......Page 286
9.4 Borzdyko's uniqueness theorem 3......Page 288
9.5 Borzdyko's uniqueness theorem 4......Page 291
10.1 Introduction......Page 293
10.2 Schwabik's uniqueness theorem......Page 297
NOTES......Page 306
REFERENCES......Page 311