Semilinear Elliptic Equations For Beginners

Author : Qing Jun Hou
Publisher :
ISBN 13 : 9781681175690
Total Pages : 242 pages
Book Rating : 4.9X/5 ( download)

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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.

Author : Marino Badiale
Publisher : Springer Science & Business Media
ISBN 13 : 0857292277
Total Pages : 204 pages
Book Rating : 4.78/5 ( download)

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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.

Author : Marino Badiale
Publisher :
ISBN 13 : 9780857292285
Total Pages : 212 pages
Book Rating : 4.85/5 ( download)

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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:

Author : Takashi Suzuki
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311055545X
Total Pages : 338 pages
Book Rating : 4.55/5 ( download)

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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.

Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814374350
Total Pages : 254 pages
Book Rating : 4.54/5 ( download)

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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.

Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814458066
Total Pages : 254 pages
Book Rating : 4.61/5 ( download)

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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.

Author : Antonio Ambrosetti
Publisher : Cambridge University Press
ISBN 13 : 9780521863209
Total Pages : 334 pages
Book Rating : 4.01/5 ( download)

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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.

Author : Ilya Kuzin
Publisher : Birkhauser
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.21/5 ( download)

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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.

Author : Ilya A. Kuzin
Publisher : Birkhäuser
ISBN 13 : 9783034892513
Total Pages : 260 pages
Book Rating : 4.19/5 ( download)

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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.

Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396050
Total Pages : 359 pages
Book Rating : 4.55/5 ( download)

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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.