Variational Methods In Nonlinear Field Equations
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Author |
: Vieri Benci |
Publisher |
: Springer |
Total Pages |
: 271 |
Release |
: 2014-10-24 |
ISBN-10 |
: 9783319069142 |
ISBN-13 |
: 3319069144 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Variational Methods in Nonlinear Field Equations by : Vieri Benci
The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.
Author |
: Vieri Benci |
Publisher |
: |
Total Pages |
: 270 |
Release |
: 2014-11-30 |
ISBN-10 |
: 3319069152 |
ISBN-13 |
: 9783319069159 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Variational Methods in Nonlinear Field Equations by : Vieri Benci
Author |
: Michael Struwe |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 288 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9783662032121 |
ISBN-13 |
: 3662032120 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Variational Methods by : Michael Struwe
Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Author |
: Dimitrios C. Kravvaritis |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 499 |
Release |
: 2020-04-06 |
ISBN-10 |
: 9783110647389 |
ISBN-13 |
: 3110647389 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Variational Methods in Nonlinear Analysis by : Dimitrios C. Kravvaritis
This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
Author |
: Philipp Grohs |
Publisher |
: Springer Nature |
Total Pages |
: 701 |
Release |
: 2020-04-03 |
ISBN-10 |
: 9783030313517 |
ISBN-13 |
: 3030313514 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Handbook of Variational Methods for Nonlinear Geometric Data by : Philipp Grohs
This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
Author |
: Michael Struwe |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 292 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783662041949 |
ISBN-13 |
: 3662041944 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Variational Methods by : Michael Struwe
Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Author |
: Dumitru Motreanu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 465 |
Release |
: 2013-11-19 |
ISBN-10 |
: 9781461493235 |
ISBN-13 |
: 1461493234 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems by : Dumitru Motreanu
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.
Author |
: Lin Li (Mathematics professor) |
Publisher |
: |
Total Pages |
: 347 |
Release |
: 2016 |
ISBN-10 |
: 9813108614 |
ISBN-13 |
: 9789813108615 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Solutions of Nonlinear Differential Equations by : Lin Li (Mathematics professor)
Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.Contents:PrefaceSome Notations and ConventionsPreliminaries and Variational PrinciplesQuasilinear Fourth-Order ProblemsKirchhoff ProblemsNonlinear Field ProblemsGradient SystemsVariable Exponent ProblemsReadership: Graduate students and researchers interested in variational methods.Key Features:Each section contains supplementary comments and bibliographical notesThe style and the choice of the material make it accessible to all newcomers to the fieldThere is a rich bibliography and an index to aid the reader
Author |
: Antonio Ambrosetti |
Publisher |
: CRC Press |
Total Pages |
: 300 |
Release |
: 1995 |
ISBN-10 |
: 288124937X |
ISBN-13 |
: 9782881249372 |
Rating |
: 4/5 (7X Downloads) |
Synopsis Variational Methods in Nonlinear Analysis by : Antonio Ambrosetti
Very Good,No Highlights or Markup,all pages are intact.
Author |
: Lin Li |
Publisher |
: Trends in Abstract and Applied Analysis |
Total Pages |
: 347 |
Release |
: 2016 |
ISBN-10 |
: 9813108606 |
ISBN-13 |
: 9789813108608 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Solutions of Nonlinear Differential Equations by : Lin Li
Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis). In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.