Semilinear Elliptic Equations For Beginners PDF Download
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Author | : Qing Jun Hou |
Publisher | : |
Total Pages | : 242 |
Release | : 2016-08-01 |
Genre | : |
ISBN | : 9781681175690 |
Download Semilinear Elliptic Equations for Beginners Book in PDF, ePub and Kindle
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.
Author | : Marino Badiale |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2010-12-07 |
Genre | : Mathematics |
ISBN | : 0857292277 |
Download Semilinear Elliptic Equations for Beginners Book in PDF, ePub and Kindle
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.
Author | : Marino Badiale |
Publisher | : |
Total Pages | : 212 |
Release | : 2011-03-30 |
Genre | : |
ISBN | : 9780857292285 |
Download Semilinear Elliptic Equations for Beginners Book in PDF, ePub and Kindle
Author | : Takashi Suzuki |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 338 |
Release | : 2020-10-12 |
Genre | : Mathematics |
ISBN | : 311055545X |
Download Semilinear Elliptic Equations Book in PDF, ePub and Kindle
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.
Author | : Philip Korman |
Publisher | : World Scientific |
Total Pages | : 254 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814374350 |
Download Global Solution Curves for Semilinear Elliptic Equations Book in PDF, ePub and Kindle
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.
Author | : Philip Korman |
Publisher | : World Scientific |
Total Pages | : 254 |
Release | : 2012-02-10 |
Genre | : Mathematics |
ISBN | : 9814458066 |
Download Global Solution Curves For Semilinear Elliptic Equations Book in PDF, ePub and Kindle
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.
Author | : Antonio Ambrosetti |
Publisher | : Cambridge University Press |
Total Pages | : 334 |
Release | : 2007-01-04 |
Genre | : Mathematics |
ISBN | : 9780521863209 |
Download Nonlinear Analysis and Semilinear Elliptic Problems Book in PDF, ePub and Kindle
A graduate text explaining how methods of nonlinear analysis can be used to tackle nonlinear differential equations. Suitable for mathematicians, physicists and engineers, topics covered range from elementary tools of bifurcation theory and analysis to critical point theory and elliptic partial differential equations. The book is amply illustrated with many exercises.
Author | : Ilya Kuzin |
Publisher | : Birkhauser |
Total Pages | : 266 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : |
Download Entire Solutions of Semilinear Elliptic Equations Book in PDF, ePub and Kindle
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.
Author | : Ilya A. Kuzin |
Publisher | : Birkhäuser |
Total Pages | : 260 |
Release | : 2012-01-06 |
Genre | : Mathematics |
ISBN | : 9783034892513 |
Download Entire Solutions of Semilinear Elliptic Equations Book in PDF, ePub and Kindle
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.
Author | : Radu Precup |
Publisher | : Walter de Gruyter |
Total Pages | : 296 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3110269058 |
Download Linear and Semilinear Partial Differential Equations Book in PDF, ePub and Kindle
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.