عنوان

Geometrical Methods in Variational Problems

شابک

9789401059558

شابک

9789401146296

شماره

b408852

عنوان اصلي

Geometrical Methods in Variational Problems

نام عام مواد

[Book]

نام نخستين پديدآور

by N. A. Bobylev, S. V. Emel'yanov, S. K. Korovin.

محل نشرو پخش و غیره

Dordrecht :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

1999.

عنوان فروست

Mathematics and Its Applications ;

مشخصه جلد

485

متن يادداشت

1 Preliminaries -- 1.1 Metric and Normed Spaces -- 1.2 Compactness -- 1.3 Linear Functional and Dual Spaces -- 1.4 Linear Operators -- 1.5 Nonlinear Operators and Functionals -- 1.6 Contraction Mapping Principle, Implicit Function Theorem, and Differential Equations on a Banach Space -- 2 Minimization of Nonlinear Functionals -- 2.1 Extrema of Smooth Functionals -- 2.2 Extremum of Lipschitzian and Convex Functionals -- 2.3 Weierstass Theorems -- 2.4 Monotonicity -- 2.5 Variational Principles -- 2.6 Additional Remarks -- 3 Homotopic Methods in Variational Problems -- 3.1 Deformations of Functionals on Hilbert Spaces -- 3.2 Deformations of Functionals on Banach Spaces -- 3.3 Global Deformations of Functionals -- 3.4 Deformation of Problems of the Calculus of Variations -- 3.5 Deformations of Lipschitzian Functions -- 3.6 Global Deformations of Lipschitzian Functions -- 3.7 Deformations of Mathematical Programming Problems -- 3.8 Deformations of Lipschitzian Functionals -- 3.9 Additional Remarks -- 4 Topological Characteristics of Extremals of Variational Problems -- 4.1 Smooth Manifolds and Differential Forms -- 4.2 Degree of Mapping -- 4.3 Rotation of Vector Fields in Finite-Dimensional Spaces -- 4.4 Vector Fields in Infinite-Dimensional Spaces -- 4.5 Computation of the Topological Index -- 4.6 Topological Index of Zero of an Isolated Minimum -- 4.7 Euler Characteristic and the Topological Index of an Isolated Critical Set -- 4.8 Topological Index of Extremals of Problems of the Calculus of Variations -- 4.9 Topological Index of Optimal Controls -- 4.10 Topological Characteristic s of Critical Points of Nonsmooth Functionals -- 4.11 Additional Remarks -- 5 Applications -- 5.1 Existence Theorems -- 5.2 Bounds of the Number of Solutions to Variational Problems -- 5.3 Applications of the Homotopic Method -- 5.4 Study of Degenerate Extremals -- 5.5 Morse Lemmas -- 5.6 Well-Posedness of Variational Problems. Ulam Problem -- 5.7 Gradient Procedures -- 5.8 Bifurcation of Extremals of Variational Problems -- 5.9 Eigenvalues of Potential Operators -- 5.10 Additional Remarks -- Bibliographical Comments -- References.

بدون عنوان

0

متن يادداشت

Since the building of all the Universe is perfect and is cre ated by the wisdom Creator, nothing arises in the Universe in which one cannot see the sense of some maXImum or mInImUm Euler God moves the Universe along geometrical lines Plato Mathematical models of most closed physical systems are based on vari ational principles, i.e., it is postulated that equations describing the evolu tion of a system are the Euler~Lagrange equations of a certain functional. In this connection, variational methods are one of the basic tools for studying many problems of natural sciences. The first problems related to the search for extrema appeared as far back as in ancient mathematics. They go back to Archimedes, Appolonius, and Euclid. In many respects, the problems of seeking maxima and minima have stimulated the creation of differential calculus; the variational prin ciples of optics and mechanics, which were discovered in the seventeenth and eighteenth centuries, gave impetus to an intensive development of the calculus of variations. In one way or another, variational problems were of interest to such giants of natural sciences as Fermat, Newton, Descartes, Euler, Huygens, 1. Bernoulli, J. Bernoulli, Legendre, Jacobi, Kepler, La grange, and Weierstrass.

شماره استاندارد بين المللي کتاب و موسيقي

9789401059558

عنوان

Springer eBooks

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Differential Equations.

موضوع مستند نشده

Global analysis.

موضوع مستند نشده

Mathematical optimization.

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Bobylev, N. A.

مستند نام اشخاص تاييد نشده

Emel'yanov, S. V.

مستند نام اشخاص تاييد نشده

Korovin, S. K.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190301082600.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y