Functional Differential Equations
Subtitle: Application of i-smooth calculus
By: by A. V. Kim
Series: Mathematics and Its Applications -- 479; Mathematics and Its Applications -- 479
Publisher: Springer Netherlands
Published: 1999
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 168
ISBN-13: 9789048152117; 9789401716307
Subjects: Differential Equations; Differential equations, partial; Functional analysis; Mathematics; Mathematical optimization; Systems theory
Description: This monograph presents the basics of i-smooth calculus, a new differential calculus of nonlinear functionals based on the notion of invariant derivative, and its application to some problems of the qualitative theory of functional differential equations. This book is unique in its separation of finite and infinite dimensional components in the structures of functional differential equations and functionals, as well as in its use of conditional representation of FDEs, which is expedient for the application of methods and constructions of i-smooth calculus. Part I contains a foundation of i-smooth calculus. Part II is an introduction to FDEs based on i-smooth calculus. Part III describes the direct Lyapunov method for systems with delays in terms of i- smooth functionals. Part IV considers an approach to the development of a dynamical programming method for systems with delays in terms of i-smooth Bellman's functionals. Audience: This volume will be of interest to students and researchers in mathematics, applied mathematicians, and engineers whose work involves ordinary differential equations, functional analysis, partial differential equations, optimal control and mathematics systems theory.
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