Integral equations and applications

Contents......Page 5
Preface......Page 7
Introduction......Page 11
1.1 Integral equations generated by problems in the theory of ordinary differential equations......Page 23
1.2 Integral equations occurring in the mathematical description of applied  problems......Page 31
1.3 Basic problems for integral equations of Volterra type (elementary  approach)......Page 40
1.4 Fredholm theory of linear integral equations with square summable  kernel......Page 51
1.5 Nonlinear equations of Hammerstein type......Page 66
Bibliographical notes......Page 71
2.1 Spaces of continuous functions......Page 74
2.2 Spaces of measurable functions......Page 81
2.3 Operators on function spaces......Page 87
2.4 Fixed point theorems; monotone operators......Page 98
Bibliographical notes......Page 102
3.1 Continuous solutions for Volterra integral equations......Page 105
3.2 Abstract Volterra equations and some special cases......Page 125
3.3 Linear Volterra equations; the resolvent and some applications......Page 141
3.4 A singular perturbation approach to abstract Volterra equations......Page 150
Bibliographical notes......Page 158
4.1 Hammerstein equations and admissibility technique......Page 161
4.2 Some problems related to resolvent kernels and applications......Page 171
4.3 Hammerstein equations on measure spaces......Page 180
4.4 Ultimate behavior of solutions to certain Volterra  functional-differential equations......Page 190
4.5 Hammerstein integrodifferential equations and boundary value  problems......Page 202
4.6 Periodic and almost periodic solutions to some integrodifferential  equations......Page 213
4.7 Integral inclusions of Volterra-Hammerstein type......Page 222
Bibliographical notes......Page 230
5 Integral equations in abstract spaces......Page 232
5.1 Equations with bounded operators......Page 233
5.2 Equations with unbounded operators in Hilbert spaces......Page 239
5.3 The semigroup method for integrodifferential equations......Page 245
5.4 A nonlinear Volterra equation and the associated semigroup of operators......Page 255
5.5 Global existence for a nonlinear integrodifferential equation in Hilbert  space......Page 271
Bibliographical notes......Page 281
6.1 An integrodifferential equation describing coagulation processes......Page 283
6.2 Optimal control processes governed by Volterra integral equations......Page 294
6.3 Stability of nuclear reactors (A)......Page 308
6.4 Stability of nuclear reactors (B)......Page 334
Bibliographical notes......Page 343
References......Page 345
Index......Page 375