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Semilinear Elliptic Equations For Beginners
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Book Synopsis Semilinear Elliptic Equations for Beginners by : Qing Jun Hou
Download or read book Semilinear Elliptic Equations for Beginners written by Qing Jun Hou and published by . This book was released on 2016-08-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semilinear Elliptic Equations for Beginners by : Marino Badiale
Download or read book Semilinear Elliptic Equations for Beginners written by Marino Badiale and published by Springer Science & Business Media. This book was released on 2010-12-07 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semilinear Elliptic Equations for Beginners by : Marino Badiale
Download or read book Semilinear Elliptic Equations for Beginners written by Marino Badiale and published by . This book was released on 2011-03-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Semilinear Elliptic Equations by : Takashi Suzuki
Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Global Solution Curves for Semilinear Elliptic Equations by : Philip Korman
Download or read book Global Solution Curves for Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Global Solution Curves For Semilinear Elliptic Equations by : Philip Korman
Download or read book Global Solution Curves For Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012-02-10 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Weak Convergence Methods For Semilinear Elliptic Equations by : Jan Chabrowski
Download or read book Weak Convergence Methods For Semilinear Elliptic Equations written by Jan Chabrowski and published by World Scientific. This book was released on 1999-10-19 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Entire Solutions of Semilinear Elliptic Equations by : Ilya Kuzin
Download or read book Entire Solutions of Semilinear Elliptic Equations written by Ilya Kuzin and published by Birkhauser. This book was released on 1997 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Entire Solutions of Semilinear Elliptic Equations by : Ilya A. Kuzin
Download or read book Entire Solutions of Semilinear Elliptic Equations written by Ilya A. Kuzin and published by Birkhäuser. This book was released on 2012-01-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Analysis and Semilinear Elliptic Problems by : Antonio Ambrosetti
Download or read book Nonlinear Analysis and Semilinear Elliptic Problems written by Antonio Ambrosetti and published by Cambridge University Press. This book was released on 2007-01-04 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear and Semilinear Partial Differential Equations by : Radu Precup
Download or read book Linear and Semilinear Partial Differential Equations written by Radu Precup and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States I by : W.-M. Ni
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States I written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium D.u + f(u) = o. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Book Synopsis An Introduction to Nonlinear Functional Analysis and Elliptic Problems by : Antonio Ambrosetti
Download or read book An Introduction to Nonlinear Functional Analysis and Elliptic Problems written by Antonio Ambrosetti and published by Springer Science & Business Media. This book was released on 2011-07-19 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Analysis and Semilinear Elliptic Problems by : Antonio Ambrosetti
Download or read book Nonlinear Analysis and Semilinear Elliptic Problems written by Antonio Ambrosetti and published by Cambridge University Press. This book was released on 2007-01-04 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semilinear Schrodinger Equations by : Thierry Cazenave
Download or read book Semilinear Schrodinger Equations written by Thierry Cazenave and published by American Mathematical Soc.. This book was released on 2003 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semilinear Elliptic Equations on IR"n by : A. K. Tertikas
Download or read book Semilinear Elliptic Equations on IR"n written by A. K. Tertikas and published by . This book was released on 1987 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Perturbation Methods and Semilinear Elliptic Problems on R^n by : Antonio Ambrosetti
Download or read book Perturbation Methods and Semilinear Elliptic Problems on R^n written by Antonio Ambrosetti and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a natural perturbation parameter, like inthe bifurcationfromthe essentialspectrum orinsingularlyperturbed equations or in the study of semiclassical standing waves for NLS. In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies. For these perturbation problems a speci?c approach,that takes advantage of such a perturbative setting, seems the most appropriate. These abstract tools are provided by perturbation methods in critical point theory. Actually, it turns out that such a framework can be used to handle a large variety of equations, usually considered di?erent in nature. Theaimofthismonographistodiscusstheseabstractmethodstogetherwith their applications to several perturbation problems, whose common feature is to n involve semilinear Elliptic Partial Di?erential Equations on R with a variational structure.
