Stability and periodic solutions of ordinary and functional differential equations.

*(English)*Zbl 0635.34001
Mathematics in Science and Engineering, Vol. 178. Orlando etc.: Academic Press, Inc., Harcourt Brace Jovanovich, Publishers. X, 337 p. (1985).

A unifying approach to the qualitative theory of ordinary differential equations, Volterra integro-differential equations and functional differential equations with bounded and infinite delay is presented. The book contains four chapters. The first one is an introduction to linear ordinary and Volterra integro-differential equations, their stability and periodic properties. Chapter 2 contains many examples of applications of all the types of considered equations. Classical examples from mechanics, but also problems involving the delays like controlling a ship, the sunflower equation, etc. The third chapter is devoted to the discussion of fixed point theorems including some recent ones on asymptotic fixed points. The fourth chapter, “Limit Sets, Periodicity and Stability”, contains a discussion for o.d.e., equations with bounded delays and Volterra equations with infinite delay. The Lyapunov’s direct method is applied to functional differential equations. Periodic solutions are obtained for them via fixed point theorems. Many results are quite recent.

Reviewer: T.Rzezachowski

##### MSC:

34-02 | Research exposition (monographs, survey articles) pertaining to ordinary differential equations |

34D20 | Stability of solutions to ordinary differential equations |

34C25 | Periodic solutions to ordinary differential equations |

34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |

34K20 | Stability theory of functional-differential equations |