An Invitation To Variational Methods In Differential Equations
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An Invitation To Variational Methods In Differential Equations
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Author : David G. Costa
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-30
An Invitation To Variational Methods In Differential Equations written by David G. Costa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-30 with Mathematics categories.
This little book is a revised and expanded version of one I wrote for the "VIII Latin American School of Mathematics" [29], in Portuguese, based on which I have periodically taught a topics course over the last 18 years. As the - graduate students tle suggests, it is an introductory text. It is addressed to of mathematics in the area of differential equations/nonlinear analysis and to mathematicians in other areas who would like to have a first exposure to so called variational methods and their applications to PDEs and ODEs. Afterwards, the reader can choose from some excellent and more compreh- sive texts, which already exist in the literature but require somewhat more maturity in the area. We present a cross section of the area of variational methods, with a m- imum (no "pun" intended) of material, but clearly illustrating through one or two examples each of the results that we have chosen to present. So, besides the first motivating chapter and an appendix, there are only ten short chapters (with three or, at most, four sections each) through which the reader is quickly exposed to a few basic aspects of the beautiful area of variational methods and applications to differential equations. In fact, the reader may initially skip some of the more technical proofs of the main theorems, concentrating instead on the applications that are given.
An Invitation To Variational Methods In Differential Equations
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Author : David Costa
language : en
Publisher: Birkhäuser
Release Date : 2010-10-22
An Invitation To Variational Methods In Differential Equations written by David Costa and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-22 with Mathematics categories.
This textbook introduces variational methods and their applications to differential equations to graduate students and researchers interested in differential equations and nonlinear analysis. It serves as a sampling of topics in critical point theory. Coverage includes: minimizations, deformations results, the mountain-pass and saddle-point theorems, critical points under constraints, and issues of compactness. Applications immediately follow each result for easy assimilation by the reader. This straightforward and systematic presentation includes many exercises and examples to motivate the study of variational methods.
An Invitation To Variational Methods In Differential Equations
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Author : David Costa
language : en
Publisher: Birkhäuser
Release Date : 2007-06-21
An Invitation To Variational Methods In Differential Equations written by David Costa and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-21 with Mathematics categories.
This textbook introduces variational methods and their applications to differential equations to graduate students and researchers interested in differential equations and nonlinear analysis. It serves as a sampling of topics in critical point theory. Coverage includes: minimizations, deformations results, the mountain-pass and saddle-point theorems, critical points under constraints, and issues of compactness. Applications immediately follow each result for easy assimilation by the reader. This straightforward and systematic presentation includes many exercises and examples to motivate the study of variational methods.
Topological And Variational Methods With Applications To Nonlinear Boundary Value Problems
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Author : Dumitru Motreanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19
Topological And Variational Methods With Applications To Nonlinear Boundary Value Problems written by Dumitru Motreanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-19 with Mathematics categories.
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
Minimax Systems And Critical Point Theory
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Author : Martin Schechter
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28
Minimax Systems And Critical Point Theory written by Martin Schechter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Mathematics categories.
This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : M. A. Lavrent’ev
language : en
Publisher: Courier Corporation
Release Date : 1989-01-01
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by M. A. Lavrent’ev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
A famous monograph with an innovative approach to classical boundary value problems, using the general basic scheme for the solution of variational problems first suggested by Hilbert and developed by Tonnelli. Directed to both mathematicians and theoreticians in mechanics.
Theory And Numerics Of Differential Equations
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Author : James Blowey
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Theory And Numerics Of Differential Equations written by James Blowey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The Ninth EPSRC Numerical Analysis Summer School was held at the Uni versity of Durharn, UK, from the 10th to the 21st of July 2000. This was the first of these schools to be held in Durharn, having previously been hosted, initially by the University of Lancaster and latterly by the University of Leicester. The purpose of the summer school was to present high quality in structional courses on topics at the forefront of numerical analysis research to postgraduate students. Eminent figures in numerical analysis presented lectures and provided high quality lecture notes. At the time of writing it is now more than two years since we first con tacted the guest speakers and during that period they have given significant portions of their time to making the summer school, and this volume, a suc cess. We would like to thank all six of them for the care which they took in the preparation and delivery of their lectures. The speakers were Christine Bernardi, Petter Bj0rstad, Carsten Carstensen, Peter Kloeden, Ralf Kornhu ber and Anders Szepessy. This volume presents written contributions from five of the six speakers. In all cases except one, these contributions are more comprehensive versions of the lecture not es which were distributed to participants during the meeting. Peter Kloeden's contribution is intended to be complementary to his lecture course and numerous references are given therein to sources of the lecture material.
An Introduction To Ordinary Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
An Introduction To Ordinary Differential Equations written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.
Aspects Of Brownian Motion
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Author : Roger Mansuy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-16
Aspects Of Brownian Motion written by Roger Mansuy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-16 with Mathematics categories.
Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.
Lectures On The Calculus Of Variations And Optimal Control Theory
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Author : L. C. Young
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-30
Lectures On The Calculus Of Variations And Optimal Control Theory written by L. C. Young and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-30 with Mathematics categories.
This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and ?automatic? existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.