Integral Equations and Applications

The Purpose Of This Book Is Threefold: To Be Used For Graduate Courses On Integral Equations; To Be A Reference For Researchers; And To Describe Methods Of Application Of The Theory. The Author Emphasizes The Role Of Volterra Equations As A Unifying Tool In The Study Of Functional Equations, And Investigates The Relation Between Abstract Volterra Equations And Other Types Of Functional-differential Equations. C. Corduneanu. Includes Bibliographical References And Index. 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

The purpose of this book is threefold: to be used for graduate courses on integral equations; to be a reference for researchers; and to describe methods of application of the theory. The author emphasizes the role of Volterra equations as a unifying tool in the study of functional equations, and investigates the relation between abstract Volterra equations and other types of functional-differential equations.