Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations

Released on by Georgiĭ Aleksandrovich Kamenskiĭ
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  • Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations Book Detail

  • Author : Georgiĭ Aleksandrovich Kamenskiĭ
  • Release Date : 2007
  • Publisher : Nova Publishers
  • Genre : Mathematics
  • Pages : 242
  • ISBN 13 : 9781600215643
  • File Size : 47,47 MB
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Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations by Georgiĭ Aleksandrovich Kamenskiĭ PDF Summary

Book Description: 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.

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Advances in Mathematics Research

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Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and compu