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Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations
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Authors: Georgii A. Kamenskii (Moscow Aviation Institute) 
Book Description:
Subject Scope: Mathematics

The nonlocal functional is an integral with the integrand depending on the unknown function at different values of the argument.
These types of functionals have different applications in
physics, engineering and sciences. The Euler type equations that arise as necessary conditions of extrema of nonlocal functionals are the functional differential equations.

The book is dedicated to systematic study of variational calculus for nonlocal functionals and to theory of boundary value problems for functional differential equations. There are described different necessary and some sufficient conditions for extrema of nonlocal functionals. Theorems of existence and uniqueness of solutions to many kinds of boundary value problems for functional differential equations are proved.

The spaces of solutions to these problems are, as a rule, Sobolev spaces
and it is not often possible to apply the analytical methods for solution of
these problems.
Therefore it is important to have approximate methods for their solution.
Different approximate methods of solution of boundary value
problems for functional differential equations and direct methods of
variational calculus for nonlocal functionals are described in the book.

The nonlocal functional is an integral with the integrand depending on the
unknown function at different values of the argument.
These types of functionals have different applications in
physics, engineering and sciences. The Euler type equations that arise as
necessary conditions of extrema of nonlocal functionals are the functional
differential equations.

The book is dedicated to systematic study of variational calculus for nonlocal
functionals and to theory of boundary value problems for functional
differential equations. There are described different necessary and some
sufficient conditions for extrema of nonlocal functionals. Theorems of
existence and uniqueness of solutions to many kinds of boundary value problems
for functional differential equations are proved.

The spaces of solutions to these problems are, as a rule, Sobolev spaces
and it is not often possible to apply the analytical methods for solution of
these problems.
Therefore it is important to have approximate methods for their solution.
Different approximate methods of solution of boundary value
problems for functional differential equations and direct methods of
variational calculus for nonlocal functionals are described in the book.

Table of Contents:
Chapter Availability

Individual chapters are available for $25 each by sending an email to novascience@earthlink.net. Nova will provide the chapter for your easy downloading or send it as an email attachment if you prefer.

Annotation

1 - Introduction; (pp. 1-6)

2 - Initial Value Problems for Functional Differential Equations;
(pp. 7-52)

3 - Symmetrical Variational Problems for Nonlocal Functionals;
(pp. 53-78)

4 - Asymmetrical Variational Problems for Nonlocal Functionals;
(pp. 79-88)

5 - Extrema of the Mixed Type Nonlocal Functionals;
(pp. 89-103)

6 - Extrema of Functionals Depending on Functions of Two Arguments;
(pp. 105-109)

7 - Boundary Value Problems for Functional Differential Equations; (pp. 111-125)

8 - Approximate Methods of Solution of Boundary Value Problems for Functional Differential Equations; (pp. 127-181)

9 - Direct Methods of Solution of Variational Problems for Nonlocal Functionals; (pp. 183-198)

10 - Addenda; (pp. 199-214)

References (pp. 215-222)
Index (pp. 223-225)

   Binding: Hardcover
   Pub. Date: 2007
   ISBN: 1-60021-564-5
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations