Introduction to The Theory of Functional Differential Equations

09.23 in Math

The aim of this book is to develop an unified approach to cover topics in the theory of functional differential equations : key questions of the general theory, boundary value problems, control problems, stability problems, calculus of variations problems, computer-assisted techniques for studying the problems mentioned.

T he central idea of applications of the theory of abstract differential equation lies in the proper choice of the such equation below.

For example, the space D of absolutely continuous functions  x : [a, b] → Rⁿ is isomorphic to the direct product of the space L of summable functions z : [a, b] → Rⁿ and the finite-dimensional space Rⁿ. Recall that the absolutely continuous function x is defined by

x(t) =_a∫^t  z(s) ds + α

where z ∈ L  α ∈ Rⁿ. The space D is Banach under the norm

||x|| _D = ||ẋ ||_L + ||x(a)||_Rⁿ

for each new problem.Only the fact that L is a Banach space is used, most of the fundamentals of the general theory such

ẋ = Fx

keep after replacement of the Lebesgue space L by an arbitrary Banach from another space.

With such general theory, such a choice permits applying standard schemes and theorems of analysis to the problems which needed previously an individual approach and special constructions. The boundary value problem is the main point of consideration. Then, it open up new opportunities for the reliable computing experiment in the study of boundary value problems as well as control problems and variational problems for square functionals in various spaces.

This book is addressed to a wide audience of scientists, post-graduate students, students, and all specialists interested in differential and functional differential equations and /or their applications.

Publisher: Hindawi Publishing Corporation
Year: 2007
Pages: 325
Format: PDF
Language: English
Size: 2.04 MB

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