Introduction to the theory of functional-differential equations. (Vvedenie v teoriyu funktsional’no-differentsial’nykh uravnenij.) (Russian. English summary) Zbl 0725.34071

Azbelev, N. V.; Maksimov, V. P.; Rakhmatullina, L. F.

Moskva: Nauka. 280 p. R. 4.70 (1991).

A general theory of functional-differential equations based on methods from functional analysis and aimed mainly at considering boundary-value problems, is systematically discussed. The monograph summarizes the viewpoint and results of a group of authors working at the Perm Polytechnics. The titles of chapters give a good idea on the content: Linear functional-differential equations; Linear boundary-value problems; Green operator; Continuous dependence of solutions to boundary-value problems on parameters; Linear delay equations; Abstract linear functional-differential equations; Reducibility of nonlinear equations; A priori estimates and solvability of reducible equations; Nonlinear boundary-value problems; Monotone operators and functional-differential inequalities; Constructive methods for linear problems; Some perspectives of applications of abstract functional-differential equations. References 187 titles.

Reviewer: A.Halanay (Bucureşti)

MSC:

34K10	Boundary value problems for functional-differential equations
34G10	Linear differential equations in abstract spaces
34K05	General theory of functional-differential equations
34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations

Keywords:

functional-differential equations; boundary-value problems; Green operator; Continuous dependence; parameters; Reducibility of nonlinear equations; A priori estimates; Monotone operators; Constructive methods