Integral Inequalities And Applications Book

	Series Editor's Preface
	Preface
	Notation
Ch. I	Scalar linear integral inequalities	1
1	Gronwall-type inequalities	1
2	Inequalities of the type of Chu and Metcalf	13
3	Applications	16
3.1	Uniqueness of the solution	17
3.2	Differentiability of the solution	17
3.3	Estimate for the Cauchy matrix of a perturbed linear equation	18
3.4	Stability of a perturbed linear equation	19
3.5	Exponential and ordinary dichotomy. Asymptotic equivalence of linear equations	20
3.6	Stability of the centre manifold	24
	Chapter I: notes and comments	27
Ch. II	Scalar nonlinear integral inequalities	29
4	Integral inequalities investigated by nonstandard methods	29
5	Bihari-type inequalities	40
6	Comparison results	53
7	Lakshmikantham's comparison method	59
8	Inequalities of the type of Deo and Dhongade	67
9	Applications	76
9.1	Two-sided estimates	76
9.2	Global existence	78
9.3	Terminal value problem	80
9.4	Stability by linear transformation	81
9.5	Perturbed nonlinear equations	85
	Chapter II: notes and comments	87
Ch. III	Analogues of Gronwall's inequality	89
10	Integral inequalities involving several integrals	89
11	Integral inequalities with iterated integrals	98
12	Integral inequalities for functions of N variables	109
13	Integro-differential inequalities	133
14	Integral inequalities with delay	142
15	Discrete inequalities	157
16	Impulse integral inequalities	181
17	Inequalities involving Stieltjes integrals	191
18	Systems of integral inequalities	196
19	Inequalities in partially ordered spaces	201
20	Applications	211
20.1	Asymptotic behaviour of solutions	211
20.2	Integro-differential equations	213
20.3	Partial differential equations	214
20.4	Functional differential equations	216
20.5	Difference equations	218
20.6	Impulse equations	223
	Chapter III: notes and comments	227
	Bibliography	229
	Author Index	243
	Subject Index	245