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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Functional Differential Equations - Application of i-smooth calculus (Hardcover, 1999 ed.)
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Functional Differential Equations - Application of i-smooth calculus (Hardcover, 1999 ed.)
Series: Mathematics and Its Applications, 479
Expected to ship within 10 - 15 working days
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Beginning with the works of N.N.Krasovskii [81, 82, 83], which
clari fied the functional nature of systems with delays, the
functional approach provides a foundation for a complete theory of
differential equations with delays. Based on the functional
approach, different aspects of time-delay system theory have been
developed with almost the same completeness as the corresponding
field of ODE (ordinary differential equations) the ory. The term
functional differential equations (FDE) is used as a syn onym for
systems with delays 1. The systematic presentation of these re
sults and further references can be found in a number of excellent
books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102,
128]. In this monograph we present basic facts of i-smooth calculus
~ a new differential calculus of nonlinear functionals, based on
the notion of the invariant derivative, and some of its
applications to the qualitative theory of functional differential
equations. Utilization of the new calculus is the main distinction
of this book from other books devoted to FDE theory. Two other
distinguishing features of the volume are the following: - the
central concept that we use is the separation of finite dimensional
and infinite dimensional components in the structures of FDE and
functionals; - we use the conditional representation of functional
differential equa tions, which is convenient for application of
methods and constructions of i~smooth calculus to FDE theory.
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