Semilinear Elliptic Equations For Beginners
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Semilinear Elliptic Equations For Beginners
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Author : Qing Jun Hou
language : en
Publisher:
Release Date : 2016-08-01
Semilinear Elliptic Equations For Beginners written by Qing Jun Hou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-01 with categories.
Elliptic equation is a class of partial differential equations describing phenomena that do not change from moment to moment, as when a flow of heat or fluid takes place within a medium with no accumulations. The Laplace equation, uxx + uyy = 0, is the simplest such equation describing this condition in two dimensions. In addition to satisfying a differential equation within the region, the elliptic equation is also determined by its values (boundary values) along the boundary of the region, which represent the effect from outside the region. Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Semilinear Elliptic Equations for Beginners is a comprehensive guide to variational methods and their applications to semilinear elliptic problems. This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains. This book will be of valuable for professors, practitioners, and researchers in mathematics and mathematical physics.
Semilinear Elliptic Equations For Beginners
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Author : Marino Badiale
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-07
Semilinear Elliptic Equations For Beginners written by Marino Badiale 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 2010-12-07 with Mathematics categories.
Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.
Semilinear Elliptic Equations For Beginners
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Author : Marino Badiale
language : en
Publisher:
Release Date : 2011-03-30
Semilinear Elliptic Equations For Beginners written by Marino Badiale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.
Semilinear Elliptic Equations
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Author : Takashi Suzuki
language : en
Publisher: de Gruyter
Release Date : 2020
Semilinear Elliptic Equations written by Takashi Suzuki and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowu
Nonlinear Analysis And Semilinear Elliptic Problems
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Author : Antonio Ambrosetti
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-04
Nonlinear Analysis And Semilinear Elliptic Problems written by Antonio Ambrosetti and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-04 with Mathematics categories.
Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.
An Introduction To Nonlinear Functional Analysis And Elliptic Problems
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Author : Antonio Ambrosetti
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-19
An Introduction To Nonlinear Functional Analysis And Elliptic Problems written by Antonio Ambrosetti 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 2011-07-19 with Mathematics categories.
This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.
Elliptic Partial Differential Equations
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Author : Lucio Boccardo
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-29
Elliptic Partial Differential Equations written by Lucio Boccardo and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Mathematics categories.
Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Djairo G De Figueiredo Selected Papers
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Author : Djairo G. de Figueiredo
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-07
Djairo G De Figueiredo Selected Papers written by Djairo G. de Figueiredo 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 2014-01-07 with Mathematics categories.
This volume presents a collection of selected papers by the prominent Brazilian mathematician Djairo G. de Figueiredo, who has made significant contributions in the area of Differential Equations and Analysis. His work has been highly influential as a challenge and inspiration to young mathematicians as well as in development of the general area of analysis in his home country of Brazil. In addition to a large body of research covering a variety of areas including geometry of Banach spaces, monotone operators, nonlinear elliptic problems and variational methods applied to differential equations, de Figueiredo is known for his many monographs and books. Among others, this book offers a sample of the work of Djairo, as he is commonly addressed, advancing the study of superlinear elliptic problems (both scalar and system cases), including questions on critical Sobolev exponents and maximum principles for non-cooperative elliptic systems in Hamiltonian form.
Semilinear Schrodinger Equations
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Author : Thierry Cazenave
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Semilinear Schrodinger Equations written by Thierry Cazenave and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.
Linear And Semilinear Partial Differential Equations
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Author : Radu Precup
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-06
Linear And Semilinear Partial Differential Equations written by Radu Precup and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.