Variational Methods For Potential Operator Equations

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Variational Methods for Potential Operator Equations

Author : Jan H. Chabrowski
Publisher : Walter de Gruyter
ISBN 13 : 3110809370
Total Pages : 301 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Variational Methods for Potential Operator Equations by : Jan H. Chabrowski

Download or read book Variational Methods for Potential Operator Equations written by Jan H. Chabrowski and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations

Author : Mordukhaĭ Moiseevich Vaĭnberg
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations by : Mordukhaĭ Moiseevich Vaĭnberg

Download or read book Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations written by Mordukhaĭ Moiseevich Vaĭnberg and published by John Wiley & Sons. This book was released on 1974 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamental Theories and Their Applications of the Calculus of Variations

Author : Dazhong Lao
Publisher : Springer Nature
ISBN 13 : 9811560706
Total Pages : 1006 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Fundamental Theories and Their Applications of the Calculus of Variations by : Dazhong Lao

Download or read book Fundamental Theories and Their Applications of the Calculus of Variations written by Dazhong Lao and published by Springer Nature. This book was released on 2020-09-02 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the calculus of variations, including fundamental theories and applications. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals.

Variational Methods in Semilinear Operator Equations

Author : Richard R. Mitchell
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Variational Methods in Semilinear Operator Equations by : Richard R. Mitchell

Download or read book Variational Methods in Semilinear Operator Equations written by Richard R. Mitchell and published by . This book was released on 1986 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation

Author : I. Chudinovich
Publisher : CRC Press
ISBN 13 : 9781584881551
Total Pages : 252 pages
Book Rating : 4.8/5 (815 download)

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Book Synopsis Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation by : I. Chudinovich

Download or read book Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation written by I. Chudinovich and published by CRC Press. This book was released on 2000-06-13 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has led modelers away from Kirchoff's classical theory for thin plates and toward increasingly refined models that yield not only the deflection of the middle section, but also account for transverse shear deformation. The improved performance of these models is achieved, however, at the expense of a much more complicated system of governing equations and boundary conditions. In this Monograph, the authors conduct a rigorous mathematical study of a number of boundary value problems for the system of partial differential equations that describe the equilibrium bending of an elastic plate with transverse shear deformation. Specifically, the authors explore the existence, uniqueness, and continuous dependence of the solution on the data. In each case, they give the variational formulation of the problems and discuss their solvability in Sobolev spaces. They then seek the solution in the form of plate potentials and reduce the problems to integral equations on the contour of the domain. This treatment covers an extensive range of problems and presents the variational method and the boundary integral equation method applied side-by-side. Readers will find that this feature of the book, along with its clear exposition, will lead to a firm and useful understanding of both the model and the methods.

Variational Methods for the Study of Nonlinear Operators

Author : Mordukhaĭ Moiseevich Vaĭnberg
Publisher :
ISBN 13 :
Total Pages : 346 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Variational Methods for the Study of Nonlinear Operators by : Mordukhaĭ Moiseevich Vaĭnberg

Download or read book Variational Methods for the Study of Nonlinear Operators written by Mordukhaĭ Moiseevich Vaĭnberg and published by . This book was released on 1964 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The subject to which this book is devoted should be of interest both to pure mathematicians and to workers in applied sciences who are increaslingly often required to deal with nonlinear systems and their associated nonlinear equations. The main subject has up to the present time appeared only in Russian journals. As the author's techniques are directed mainly towards proving existence theorems (largely concerning nonlinear integral operators), rather than developing techniques for the actual solution of nonlinear equations, it was thought the addition of the last chapter of the Russian book "Functional analysis in normed spaces" by L.V. Kantorovich and G.P. Akilov devoted to the extension of Newton's method to nonlinear functional equations would substantially increase the usefulness of this translation"--Translator's preface.

Methods for Solving Operator Equations

Author : V. P. Tanana
Publisher : Walter de Gruyter
ISBN 13 : 3110900157
Total Pages : 229 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Methods for Solving Operator Equations by : V. P. Tanana

Download or read book Methods for Solving Operator Equations written by V. P. Tanana and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Variational Principles and Methods in Theoretical Physics and Chemistry

Author : Robert K. Nesbet
Publisher : Cambridge University Press
ISBN 13 : 1139435698
Total Pages : 245 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Variational Principles and Methods in Theoretical Physics and Chemistry by : Robert K. Nesbet

Download or read book Variational Principles and Methods in Theoretical Physics and Chemistry written by Robert K. Nesbet and published by Cambridge University Press. This book was released on 2002-11-14 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly suitable as a backup reference for lecture courses in mathematical methods in physics and theoretical chemistry.

Variational Methods in Mathematics, Science and Engineering

Author : Karel Rektorys
Publisher : Springer Science & Business Media
ISBN 13 : 9401164509
Total Pages : 566 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Variational Methods in Mathematics, Science and Engineering by : Karel Rektorys

Download or read book Variational Methods in Mathematics, Science and Engineering written by Karel Rektorys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: The impulse which led to the writing of the present book has emerged from my many years of lecturing in special courses for selected students at the College of Civil Engineering of the Tech nical University in Prague, from experience gained as supervisor and consultant to graduate students-engineers in the field of applied mathematics, and - last but not least - from frequent consultations with technicians as well as with physicists who have asked for advice in overcoming difficulties encountered in solving theoretical problems. Even though a varied combination of problems of the most diverse nature was often in question, the problems discussed in this book stood forth as the most essential to this category of specialists. The many discussions I have had gave rise to considerations on writing a book which should fill the rather unfortunate gap in our literature. The book is designed, in the first place, for specialists in the fields of theoretical engineering and science. However, it was my aim that the book should be of interest to mathematicians as well. I have been well aware what an ungrateful task it may be to write a book of the present type, and what problems such an effort can bring: Technicians and physicists on the one side, and mathematicians on the other, are often of diametrically opposing opinions as far as books con ceived for both these categories are concerned.

__________

Author : V. M. Filippov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898246
Total Pages : 260 pages
Book Rating : 4.8/5 (982 download)

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Book Synopsis __________ by : V. M. Filippov

Download or read book __________ written by V. M. Filippov and published by American Mathematical Soc.. This book was released on 1989-12-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a variational method for solving linear equations with $B$-symmetric and $B$-positive operators and generalizes the method to nonlinear equations with nonpotential operators. The author carries out a constructive extension of the variational method to ``nonvariational'' equations (including parabolic equations) in classes of functionals which differ from the Euler-Lagrange functionals. In this connection, some new functions spaces are considered. Intended for mathematicians working in the areas of functional analysis and differential equations, this book would also prove useful for researchers in other areas and students in advanced courses who use variational methods in solving linear and nonlinear boundary value problems in continuum mechanics and theoretical physics.

Variational Methods in Mathematical Physics

Author : Philippe Blanchard
Publisher : Springer
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Variational Methods in Mathematical Physics by : Philippe Blanchard

Download or read book Variational Methods in Mathematical Physics written by Philippe Blanchard and published by Springer. This book was released on 1992-06-04 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. A comprehensive bibliography and index round out the work.

Measure and Integration Theory

Author : Heinz Bauer
Publisher : Walter de Gruyter
ISBN 13 : 311086620X
Total Pages : 249 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Measure and Integration Theory by : Heinz Bauer

Download or read book Measure and Integration Theory written by Heinz Bauer and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.

Weak Convergence Methods for Semilinear Elliptic Equations

Author : Jan Chabrowski
Publisher : World Scientific
ISBN 13 : 9789810240769
Total Pages : 256 pages
Book Rating : 4.2/5 (47 download)

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Book Synopsis Weak Convergence Methods for Semilinear Elliptic Equations by : Jan Chabrowski

Download or read book Weak Convergence Methods for Semilinear Elliptic Equations written by Jan Chabrowski and published by World Scientific. This book was released on 1999 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrdinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais-Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration-compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik-Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions.

Linking Methods in Critical Point Theory

Author : Martin Schechter
Publisher : Springer Science & Business Media
ISBN 13 : 146121596X
Total Pages : 305 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linking Methods in Critical Point Theory by : Martin Schechter

Download or read book Linking Methods in Critical Point Theory written by Martin Schechter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the Trans-Canada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on ...

Variational Methods in Theoretical Mechanics

Author : J.T. Oden
Publisher : Springer Science & Business Media
ISBN 13 : 3642963129
Total Pages : 313 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Variational Methods in Theoretical Mechanics by : J.T. Oden

Download or read book Variational Methods in Theoretical Mechanics written by J.T. Oden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .

Variational Methods with Applications in Science and Engineering

Author : Kevin W. Cassel
Publisher : Cambridge University Press
ISBN 13 : 1107067375
Total Pages : 433 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Variational Methods with Applications in Science and Engineering by : Kevin W. Cassel

Download or read book Variational Methods with Applications in Science and Engineering written by Kevin W. Cassel and published by Cambridge University Press. This book was released on 2013-07-22 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Contributions to Nonlinear Analysis

Author : Thierry Cazenave
Publisher : Springer Science & Business Media
ISBN 13 : 3764374012
Total Pages : 516 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Contributions to Nonlinear Analysis by : Thierry Cazenave

Download or read book Contributions to Nonlinear Analysis written by Thierry Cazenave and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t n where ? is a bounded domain of R ,n? 1, with a smooth boundary ? = ? ?? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u ?? u =?f (u)in? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.