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. |