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: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12

Semilinear Elliptic Equations written by Takashi Suzuki and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 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, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.

Global Solution Curves For Semilinear Elliptic Equations

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Author : Philip Korman
language : en
Publisher: World Scientific
Release Date : 2012-02-10

Global Solution Curves For Semilinear Elliptic Equations written by Philip Korman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-10 with Mathematics categories.

This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.

Entire Solutions Of Semilinear Elliptic Equations

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Author : Ilya Kuzin
language : en
Publisher: Birkhauser
Release Date : 1997

Entire Solutions Of Semilinear Elliptic Equations written by Ilya Kuzin and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to physics and other sciences. This book presents a wealth of modern methods to solve such equations, including the systematic use of the Pohozaev identities for the description of sharp estimates for radial solutions and the fibring method. Existence results for equations with supercritical growth and non-zero right-hand sides are given.Readers of this exposition will be advanced students and researchers in mathematics, physics and other sciences who want to learn about specific methods to tackle problems involving semilinear elliptic equations.

Global Solution Curves For Semilinear Elliptic Equations

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Author : Philip Korman
language : en
Publisher: World Scientific
Release Date : 2012

Global Solution Curves For Semilinear Elliptic Equations written by Philip Korman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.

Entire Solutions Of Semilinear Elliptic Equations

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Author : Ilya A. Kuzin
language : en
Publisher: Birkhäuser
Release Date : 2012-01-06

Entire Solutions Of Semilinear Elliptic Equations written by Ilya A. Kuzin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-06 with Mathematics categories.

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

Weak Convergence Methods For Semilinear Elliptic Equations

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Author : Jan Chabrowski
language : en
Publisher: World Scientific
Release Date : 1999-10-19

Weak Convergence Methods For Semilinear Elliptic Equations written by Jan Chabrowski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-19 with Mathematics categories.

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 Schrödinger 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.

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.