Extrema Of Nonlocal Functionals And Boundary Value Problems For Functional Differential Equations

Extrema of Nonlocal Functionals and Boundary Value Problems for Functional 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.

Advances in Mathematics Research

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.

Functional Differential Equations