Applied theory of functional differential equations. (English) Zbl 0785.34005

Kolmanovskij, V.; Myshkis, A.

Mathematics and Its Applications. Soviet Series. 85. Dordrecht: Kluwer Academic Publishers. xv, 234 p. (1992).

The book is mainly devoted to stability and optimal control for retarded and neutral differential equations, both deterministic and stochastic. Chapter 3, Stability of retarded differential equations, pp. 97-124, Chapter 4, Stability of neutral type functional differential equations, pp. 125-136, Chapter 5, Stability of stochastic functional differential equations, pp. 137-150, Chapter 6, Problems of control for deterministic FDEs, pp. 151-173, Chapter 7, Optimal control of stochastic delay systems, pp. 173-182, Chapter 8, State estimates of stochastic systems with delay, pp. 183-198. Chapter 2 is devoted to the presentation of the general theory, pp. 35-96, including 12 pages describing a Hopf bifurcation problem, while the first chapter, pp. 1-34, describes a lot of models from various fields leading to functional differential equations. The references (33 pages) refer to 535 authors, some of them with several titles. Index.

Reviewer: A.Halanay (Bucureşti)

MSC:

34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34K05	General theory of functional-differential equations
34K99	Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K20	Stability theory of functional-differential equations
34K35	Control problems for functional-differential equations
34K40	Neutral functional-differential equations
34K50	Stochastic functional-differential equations
49J25	Optimal control problems with equations with ret. arguments (exist.) (MSC2000)

Keywords:

stability; optimal control; retarded and neutral differential equations; stochastic; Hopf bifurcation