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Author: Georgiĭ Aleksandrovich Kamenskiĭ
Publisher: Nova Publishers
ISBN: 9781600215643
Category : Mathematics
Languages : en
Pages : 242
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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.
Author: Georgiĭ Aleksandrovich Kamenskiĭ
Publisher: Nova Publishers
ISBN: 9781600215643
Category : Mathematics
Languages : en
Pages : 242
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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.
Author: Gabriel Oyibo
Publisher: Nova Publishers
ISBN: 9781590335185
Category : Mathematics
Languages : en
Pages : 182
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Book Description
Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics. Contents: Preface; Solvability of Quasilinear Elliptic Second Order Differential Equations in Rn without Condition at Infinity; Recent Topics on a Class of Nonlinear Integrodifferential Equations of Physical Significance'; Nonparametric Estimation with Censored Observations; Normalisers of Groups Commensurable with PSL2(Z); Spectral Analysis of a Class of Multigroup Neutron Transport Operators in Slab Geometry; Extremum of a Nonlocal Functional Depending on Higher Order Derivatives of the Unknown Function; On Quantum Conditional Probability Spaces; Index.
Author: Donald Greenspan
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
A combination variational-difference numerical method, applied recently to a large variety of nonlinear boundary value problems, is studied from the points of view of convergence and possible generalizations. The essence of the method lies in minimizing a functional numerically rather than in approximating the solution of the Euler differential equation of the functional. (Author).
Author: Bashir Ahmad
Publisher: World Scientific
ISBN: 9811230420
Category : Mathematics
Languages : en
Pages : 597
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Book Description
There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.
Author:
Publisher:
ISBN:
Category : Functional differential equations
Languages : en
Pages : 494
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Book Description
Author: Guo Chun Wen
Publisher: World Scientific
ISBN: 981454311X
Category : Science
Languages : en
Pages : 338
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Book Description
In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.
Author: G. W. Reddien
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 52
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Book Description
Author: Jian-ke Lu
Publisher: World Scientific
ISBN: 9814518026
Category : Mathematics
Languages : en
Pages : 482
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Book Description
This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincaré-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
Author:
Publisher:
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 560
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Book Description
Author: Donald Greenspan
Publisher:
ISBN:
Category : Functionals
Languages : en
Pages : 28
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Book Description
