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| Title: | Extrema of Non-local Functionals & Boundary Value Problems for Functional Differential Equations
|
| Author: | Georgii A Kamenskii |
| ISBN: | 1600215645 : 9781600215643 |
| Illustrations: | tables & charts |
| Format: | Hardback |
| Size: | 180x260mm |
| Pages: | 225 |
| Weight: | .66 Kg. |
| Published: | Nova Science Publishers - September 2007 |
| List Price: | 59.5 Pounds Sterling |
| Availability: | In Print |
| Subjects: | Differential equations |
The non-local 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 non-local functionals are the functional differential equations. The book is dedicated to systematic study of variational calculus for non-local functionals and to theory of boundary value problems for functional differential equations. There are described different necessary and some sufficient conditions for extrema of non-local 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 non-local functionals are described in the book. The non-local 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 non-local functionals are the functional differential equations. The book is dedicated to systematic study of variational calculus for non-local functionals and to theory of boundary value problems for functional differential equations. There are described different necessary and some sufficient conditions for extrema of non-local 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 non-local functionals are described in the book.
Introduction; Initial Value Problems for Functional Differential Equations; Symmetrical Variational Problems for Non-local Functionals; Asymmetrical Variational Problems for Non-local Functionals; Extrema of the Mixed Type Non-local Functionals; Extrema of Functionals Depending on Functions of Two Arguments; Boundary Value Problems for Functional Differential Equations; Approximate Methods of Solution of Boundary Value Problems for Functional Differential Equations; Direct Methods of Solution of Variational Problems for Non-local Functionals; Addenda; Index.
