Uniqueness and nonuniqueness criteria for ordinary differential equations

Description

This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions Content: Ch. 1. First Order Differential Equations -- 1.2. Lipschitz uniqueness theorem -- 1.3. Peano's uniqueness theorem -- 1.4. Osgood's uniqueness theorem -- 1.5. Montel -- Tonelli's uniqueness theorem -- 1.6. Nagumo's uniqueness theorem -- 1.7. Krasnosel'skii -- Krein's uniqueness theorem -- 1.8. Kooi's uniqueness theorem -- 1.9. Roger's uniqueness theorem -- 1.10. Witte's uniqueness theorem -- 1.11. Perron's uniqueness theorem -- 1.12. Gyori's uniqueness theorem -- 1.13. Iyanaga's uniqueness theorem -- 1.14. Inaba's uniqueness theorem -- 1.15. Kamke's uniqueness theorem -- 1.16. Shen's uniqueness theorem -- 1.17. Mikolajska's uniqueness theorem -- 1.18. Brauer's uniqueness theorem -- 1.19. Wend's uniqueness theorem -- 1.20. van Kampen's uniqueness theorem -- 1.21. Yosie's uniqueness theorem -- 1.22. Kitagawa's uniqueness theorem -- 1.23. Tamarkine's nonuniqueness theorem -- 1.24. Lakshmikantham's nonuniqueness theorem -- 1.25. Samimi's nonuniqueness theorem -- Ch. 2. First Order Differential Equations (Contd.) -- 2.2. Lipschitz uniqueness theorem -- 2.3. Nagumo's uniqueness theorem -- 2.4. Krasnosel'skii -- Krein's uniqueness theorem -- 2.5. Boruvka's uniqueness theorem -- 2.6. Wend's uniqueness theorem -- 2.7. Zabreiko's uniqueness theorem -- 2.8. Lakshmikantham's uniqueness theorem -- 2.9. Bownds' uniqueness theorem -- 2.10. Bownds -- Metcalf's uniqueness theorem -- 2.11. Gard's uniqueness theorem -- 2.12. Majorana's nonuniqueness theorem -- Ch. 3. First Order Differential Systems -- 3.2. Lipschitz uniqueness theorem -- 3.3. Peano's uniqueness theorem -- 3.4. Heins' uniqueness theorem -- 3.5. Giuliano's uniqueness theorem -- 3.6. Nagumo's uniqueness theorem -- 3.7. Witte's uniqueness theorem -- 3.8. Kamke's uniqueness theorem -- 3.9. Wend's uniqueness theorem -- 3.10. Bownds' uniqueness theorem -- 3.11. Gard's uniqueness theorem -- 3.12. Driver -- Norris' uniqueness theorem -- 3.13. Goebel -- Zur's uniqueness theorem -- 3.14. Bownds -- Diaz's uniqueness theorem -- 3.15. Okamura's uniqueness theorem -- 3.16. Chu -- Diaz's uniqueness theorem -- 3.17. Sato's uniqueness theorem -- 3.18. Brauer -- Sternberg's uniqueness theorem -- 3.19. Moyer's uniqueness theorem -- 3.20. Bernfeld -- Driver -- Lakshmikantham's uniqueness theorem -- 3.21. Kaper -- Kwong's uniqueness theorem -- 3.22. Tesarova -- Dosly's uniqueness theorem -- 3.23. Antosiewicz's uniqueness theorem -- 3.24. Lakshmikantham -- Samimi's uniqueness theorem -- 3.25. Kalas' nonuniqueness theorem -- 3.26. Samimi's nonuniqueness theorem -- Ch. 4. Higher Order Differential Equations -- 4.2. Lipschitz uniqueness theorem -- 4.3. Merli's uniqueness theorem -- 4.4. Kikodze's uniqueness theorem -- 4.5. Wend's uniqueness theorem -- 4.6. Redheffer's uniqueness theorem -- 4.7. Heidel's uniqueness theorem -- Ch. 5. Differential Equations in Abstract Spaces -- 5.2. Aziz -- Diaz's uniqueness theorem -- 5.3. Medeiros' uniqueness theorem -- 5.4. Diaz -- Weinacht's uniqueness theorem -- 5.5. Perron's uniqueness theorem -- 5.6. Olech's uniqueness theorem -- 5.7. Goldstein's uniqueness theorem -- 5.8. Arrate's uniqueness theorem -- 5.9. Ramankutty's uniqueness theorem -- 5.10. Murakami's uniqueness theorem -- 5.11. Lakshmikantham's uniqueness theorem -- Ch. 6. Complex Differential Equations -- 6.2. Deo -- Lakshmikantham's uniqueness theorem -- Ch. 7. Functional Differential Equations -- 7.2. Lakshmikantham's uniqueness theorem -- 7.3. Lakshmikantham -- Leela's uniqueness theorem -- 7.4. Lakshmikantham -- Shendge's uniqueness theorem -- 7.5. Furumochi's uniqueness theorem -- Ch. 8. Impulsive Differential Equations -- 8.2. Hu -- Lakshmikantham's uniqueness theorem -- 8.3. Pandit's uniqueness theorem -- Ch. 9. Differential Equations with Hysteresis -- 9.2. Borzdyko's uniqueness theorem 1 -- 9.3. Borzdyko's uniqueness theorem 2 -- 9.4. Borzdyko's uniqueness theorem 3 -- 9.5. Borzdyko's uniqueness theorem 4 -- Ch. 10. Generalized Differential Equations -- 10.2. Schwabik's uniqueness theorem.