Uniqueness And Nonuniqueness Criteria For Ordinary Differential EquationsThis 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. |
Contents
| 1 | |
CHAPTER 2 FIRST ORDER DIFFERENTIAL EQUATIONS CONTD | 102 |
CHAPTER 3 FIRST ORDER DIFFERENTIAL SYSTEMS | 134 |
CHAPTER 4 HIGHER ORDER DIFFERENTIAL EQUATIONS | 204 |
CHAPTER 5 DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES | 225 |
CHAPTER 6 COMPLEX DIFFERENTIAL EQUATIONS | 248 |
CHAPTER 7 FUNCTIONAL DIFFERENTIAL EQUATIONS | 251 |
CHAPTER 8 IMPULSIVE DIFFERENTIAL EQUATIONS | 263 |
CHAPTER 9 DIFFERENTIAL EQUATIONS WITH HYSTERESIS | 272 |
CHAPTER 10 GENERALIZED DIFFERENTIAL EQUATIONS | 282 |
NOTES | 295 |
REFERENCES | 300 |
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Common terms and phrases
absolutely continuous Banach space Caratheodory conditions classical abstract solution conditions of Theorem Consider the initial constant continuous and nonnegative continuous function continuous in S+ continuously differentiable contradiction Corollary defined and continuous differentiable function differential inequality Example exists a Lyapunov extended solution finite following result function f(x Further hence Henstock integral hypothesis implies initial value problem interval xo Kamke's Uniqueness Theorem Kurzweil Lebesgue Lemma Let f(x Let f(x,y Let the function lim sup limo+ Lipschitz condition 1.2.1 Lipschitz Uniqueness Theorem Lyapunov function Math maximal solution mean value theorem nondecreasing nonincreasing ordinary differential equations P₁ positive number proof of Theorem satisfies the conditions satisfies the inequality satisfies the Lipschitz sequence solution in xo solutions of 1.1.1 sufficiently small Suppose that y(x Suppose y(x unique solution V.Lakshmikantham value problem 1.1.1 xo+a y(xo yn(x yo(x zero ξο ψ(το