Volterra integral and differential equations. 2nd ed. (English) Zbl 1075.45001

Mathematics in Science and Engineering 202. Amsterdam: Elsevier (ISBN 0-444-51786-3/hbk). x, 353 p. (2005).
[For the first edition (1983) see Zbl 0515.45001.]
This is the second edition of the author’s book on Volterra integral and differential equations. The main approach is to consider those Volterra equations that can be treated as perturbations of ordinary differential equations and there is a very strong emphasis on Lyapunov functions.
Chapter 1 gives a gentle introduction to the subject and discusses integral equations reducible to ordinary differential equations. In chapter 2 linear equations are studied and various stability concepts introduced. In chapter 3 the basic existence, uniqueness and continuation results are established and chapter 4 treats the history and motivating examples of the theory. In chapters 5 and 6 Lyapunov’s method is used to derive results about stability, instability and boundedness of the solutions. Chapter 7 which is to a large part new in this edition considers the theory of resolvents and chapter 8 is a treatment of functional differential equations.


45D05 Volterra integral equations
45J05 Integro-ordinary differential equations
34K05 General theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
45M05 Asymptotics of solutions to integral equations
45M10 Stability theory for integral equations
45M15 Periodic solutions of integral equations
45-02 Research exposition (monographs, survey articles) pertaining to integral equations
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
45G10 Other nonlinear integral equations
45-03 History of integral equations
92D25 Population dynamics (general)


Zbl 0515.45001