Entire Solutions Of Semilinear Elliptic Equations

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Entire Solutions of Semilinear Elliptic Equations

Author : Ilya Kuzin
Publisher : Birkhauser
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.3/5 (91 download)

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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.

Entire Solutions of Semilinear Elliptic Equations

Author : Ilya A. Kuzin
Publisher : Birkhäuser
ISBN 13 : 9783034892513
Total Pages : 260 pages
Book Rating : 4.8/5 (925 download)

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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.

Entire Solutions of Semilinear Elliptic Equations

Author : Ilya A. Kuzin
Publisher : Birkhäuser
ISBN 13 : 3034892500
Total Pages : 254 pages
Book Rating : 4.0/5 (348 download)

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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 2012-12-06 with total page 254 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.

Global Solution Curves for Semilinear Elliptic Equations

Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814374350
Total Pages : 254 pages
Book Rating : 4.8/5 (143 download)

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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.

Nonlinear Diffusion Equations and Their Equilibrium States I

Author : W.-M. Ni
Publisher : Springer
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.3/5 (91 download)

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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. This book was released on 1988-06-24 with total page 384 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.

Global Solution Curves for Semilinear Elliptic Equations

Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814458066
Total Pages : 256 pages
Book Rating : 4.8/5 (144 download)

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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 256 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. Contents:Curves of Solutions on General Domains:Continuation of SolutionsSymmetric Domains in R2Turning Points and the Morse IndexConvex Domains in R2Pohozaev's Identity and Non-Existence of Solutions for Elliptic SystemsProblems at ResonanceCurves of Solutions on Balls:Preliminary ResultsPositivity of Solution to the Linearized ProblemUniqueness of the Solution CurveDirection of a Turn and Exact MultiplicityOn a Class of Concave-Convex EquationsMonotone Separation of GraphsThe Case of Polynomial ƒ(u) in Two DimensionsThe Case When ƒ(0) < 0Symmetry BreakingSpecial EquationsOscillations of the Solution CurveUniqueness for Non-Autonomous ProblemsExact Multiplicity for Non-Autonomous ProblemsNumerical Computation of SolutionsRadial Solutions of Neumann ProblemGlobal Solution Curves for a Class of Elliptic SystemsThe Case of a “Thin” AnnulusA Class of p-Laplace ProblemsTwo Point Boundary Value Problems:Positive Solutions of Autonomous ProblemsDirection of the TurnStability and Instability of SolutionsS-Shaped Solution CurvesComputing the Location and the Direction of BifurcationA Class of Symmetric NonlinearitiesGeneral NonlinearitiesInfinitely Many Curves with Pitchfork BifurcationAn Oscillatory Bifurcation from Zero: A Model ExampleExact Multiplicity for Hamiltonian SystemsClamped Elastic Beam EquationSteady States of Convective EquationsQuasilinear Boundary Value ProblemsThe Time Map for Quasilinear EquationsUniqueness for a p-Laplace Case Readership: Graduate students and researchers in analysis and differential equations, and numerical analysis and computational mathematics. Keywords:Global Solution Curves;Exact MultiplicityKey Features:Integration of theoretical study of exact multiplicity results with numerical analysis and computationIncludes computing bifurcation diagramsPresents several computer-assisted proofs of uniqueness and exact multiplicity theoremsComputations using power series

Semilinear Elliptic Equations for Beginners

Author : Marino Badiale
Publisher : Springer Science & Business Media
ISBN 13 : 0857292277
Total Pages : 204 pages
Book Rating : 4.8/5 (572 download)

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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.

Semilinear Elliptic Equations

Author : Takashi Suzuki
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311055545X
Total Pages : 338 pages
Book Rating : 4.1/5 (15 download)

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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.

Selected Papers on Analysis and Differential Equations

Author : 野水克己
Publisher : American Mathematical Soc.
ISBN 13 : 9780821835081
Total Pages : 152 pages
Book Rating : 4.8/5 (35 download)

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Book Synopsis Selected Papers on Analysis and Differential Equations by : 野水克己

Download or read book Selected Papers on Analysis and Differential Equations written by 野水克己 and published by American Mathematical Soc.. This book was released on 2003 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal, Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including nonlinear partial differential equations, $C*$-algebras, and Schrodinger operators. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Semilinear Elliptic Equations

Author : Takashi Suzuki
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110556286
Total Pages : 490 pages
Book Rating : 4.1/5 (15 download)

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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 490 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.

Canadian Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Mathematics by :

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1988-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory and Applications of Differentiable Functions of Several Variables

Author : Lev Dmitrievich Kudri︠a︡vt︠s︡ev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821803387
Total Pages : 300 pages
Book Rating : 4.8/5 (33 download)

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Book Synopsis Theory and Applications of Differentiable Functions of Several Variables by : Lev Dmitrievich Kudri︠a︡vt︠s︡ev

Download or read book Theory and Applications of Differentiable Functions of Several Variables written by Lev Dmitrievich Kudri︠a︡vt︠s︡ev and published by American Mathematical Soc.. This book was released on 1994 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to Sergei Mikhailovich Nikol'skii on the occasion of his eighty-fifth birthday. The collection contains new results on the following topics: approximation of functions, imbedding theory, interpolation of function spaces, convergence of series in trigonometric and general orthogonal systems, quasilinear elliptic problems, spectral theory of nonselfadjoint operators, asymptotic properties of pseudodifferential operators, and methods of approximate solution of Laplace's equation.

European Congress of Mathematics

Author : Carles Casacuberta
Publisher : Birkhäuser
ISBN 13 : 3034882688
Total Pages : 611 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis European Congress of Mathematics by : Carles Casacuberta

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.

The Fractional Laplacian

Author : Wenxiong Chen
Publisher : World Scientific
ISBN 13 : 9813224010
Total Pages : 342 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Fractional Laplacian by : Wenxiong Chen

Download or read book The Fractional Laplacian written by Wenxiong Chen and published by World Scientific. This book was released on 2020-06-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.

Elliptic Systems of Phase Transition Type

Author : Nicholas D. Alikakos
Publisher : Springer
ISBN 13 : 3319905724
Total Pages : 343 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Elliptic Systems of Phase Transition Type by : Nicholas D. Alikakos

Download or read book Elliptic Systems of Phase Transition Type written by Nicholas D. Alikakos and published by Springer. This book was released on 2019-01-21 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin's proof. It also introduces an alternative method for obtaining pointwise estimates. Key features and topics of this self-contained, systematic exposition include: • Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions. • Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves. • Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates. • Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results. This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.

Canadian Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Mathematics by :

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1991-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations and Their Equilibrium States II

Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396085
Total Pages : 364 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by : W.-M. Ni

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 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 = ~U + f(u). Here ~ 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 ~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.