Perturbation Results For Semilinear Elliptic Equations In R N

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Perturbation Methods and Semilinear Elliptic Problems on R^n

Author : Antonio Ambrosetti
Publisher : Springer Science & Business Media
ISBN 13 : 3764373962
Total Pages : 187 pages
Book Rating : 4.7/5 (643 download)

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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.

Weak Convergence Methods For Semilinear Elliptic Equations

Author : Jan Chabrowski
Publisher : World Scientific
ISBN 13 : 9814494267
Total Pages : 247 pages
Book Rating : 4.8/5 (144 download)

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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.

Solutions Of Nonlinear Differential Equations: Existence Results Via The Variational Approach

Author : Lin Li
Publisher : World Scientific
ISBN 13 : 9813108622
Total Pages : 362 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Solutions Of Nonlinear Differential Equations: Existence Results Via The Variational Approach by : Lin Li

Download or read book Solutions Of Nonlinear Differential Equations: Existence Results Via The Variational Approach written by Lin Li and published by World Scientific. This book was released on 2016-04-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.

Topics in Nonlinear Analysis

Author : Joachim Escher
Publisher : Birkhäuser
ISBN 13 : 3034887655
Total Pages : 741 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Topics in Nonlinear Analysis by : Joachim Escher

Download or read book Topics in Nonlinear Analysis written by Joachim Escher and published by Birkhäuser. This book was released on 2012-12-06 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herbert Amann's work is distinguished and marked by great lucidity and deep mathematical understanding. The present collection of 31 research papers, written by highly distinguished and accomplished mathematicians, reflect his interest and lasting influence in various fields of analysis such as degree and fixed point theory, nonlinear elliptic boundary value problems, abstract evolutions equations, quasi-linear parabolic systems, fluid dynamics, Fourier analysis, and the theory of function spaces. Contributors are A. Ambrosetti, S. Angenent, W. Arendt, M. Badiale, T. Bartsch, Ph. Bénilan, Ph. Clément, E. Faöangová, M. Fila, D. de Figueiredo, G. Gripenberg, G. Da Prato, E.N. Dancer, D. Daners, E. DiBenedetto, D.J. Diller, J. Escher, G.P. Galdi, Y. Giga, T. Hagen, D.D. Hai, M. Hieber, H. Hofer, C. Imbusch, K. Ito, P. Krejcí, S.-O. Londen, A. Lunardi, T. Miyakawa, P. Quittner, J. Prüss, V.V. Pukhnachov, P.J. Rabier, P.H. Rabinowitz, M. Renardy, B. Scarpellini, B.J. Schmitt, K. Schmitt, G. Simonett, H. Sohr, V.A. Solonnikov, J. Sprekels, M. Struwe, H. Triebel, W. von Wahl, M. Wiegner, K. Wysocki, E. Zehnder and S. Zheng.

Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1001 pages
Book Rating : 4./5 ( download)

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Book Synopsis by :

Download or read book written by and published by World Scientific. This book was released on with total page 1001 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Variational Methods for Nonlocal Fractional Problems

Author : Giovanni Molica Bisci
Publisher : Cambridge University Press
ISBN 13 : 1316571696
Total Pages : 401 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Variational Methods for Nonlocal Fractional Problems by : Giovanni Molica Bisci

Download or read book Variational Methods for Nonlocal Fractional Problems written by Giovanni Molica Bisci and published by Cambridge University Press. This book was released on 2016-03-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

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.

Journal of Partial Differential Equations

Author :
Publisher :
ISBN 13 :
Total Pages : 808 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Journal of Partial Differential Equations by :

Download or read book Journal of Partial Differential Equations written by and published by . This book was released on 1995 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hamiltonian Dynamics and Celestial Mechanics

Author : Donald Saari
Publisher : American Mathematical Soc.
ISBN 13 : 0821805665
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Hamiltonian Dynamics and Celestial Mechanics by : Donald Saari

Download or read book Hamiltonian Dynamics and Celestial Mechanics written by Donald Saari and published by American Mathematical Soc.. This book was released on 1996 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The symbiotic of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.

Geometric Analysis and PDEs

Author : Matthew J. Gursky
Publisher : Springer
ISBN 13 : 364201674X
Total Pages : 296 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Geometric Analysis and PDEs by : Matthew J. Gursky

Download or read book Geometric Analysis and PDEs written by Matthew J. Gursky and published by Springer. This book was released on 2009-07-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Global Solution Curves for Semilinear Elliptic Equations

Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814374342
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.

A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials

Author : Florica C. Cîrstea
Publisher : American Mathematical Soc.
ISBN 13 : 0821890220
Total Pages : 97 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials by : Florica C. Cîrstea

Download or read book A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials written by Florica C. Cîrstea and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.

Modern Problems in PDEs and Applications

Author : Marianna Chatzakou
Publisher : Springer Nature
ISBN 13 : 3031567323
Total Pages : 187 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Modern Problems in PDEs and Applications by : Marianna Chatzakou

Download or read book Modern Problems in PDEs and Applications written by Marianna Chatzakou and published by Springer Nature. This book was released on 2024 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of the volume is gathering all the contributions given by the speakers (mini courses) and some of the participants (short talks) of the summer school "Modern Problems in PDEs and Applications" held at the Ghent Analysis and PDE Center from 23 August to 2 September 2023. The school was devoted to the study of new techniques and approaches for solving partial differential equations, which can either be considered or arise from the physical point of view or the mathematical perspective. Both sides are extremely important since theories and methods can be developed independently, aiming to gather each other in a common objective. The aim of the summer school was to progress and advance in the problems considered. Note that real-world problems and their applications are classical study trends in physical or mathematical modelling. The summer school was organised in a friendly atmosphere and synergy, and it was an excellent opportunity to promote and encourage the development of the subject in the community.

Advances in Differential Equations

Author :
Publisher :
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Advances in Differential Equations by :

Download or read book Advances in Differential Equations written by and published by . This book was released on 2006 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topological Methods, Variational Methods and Their Applications

Author : Haim Brzis
Publisher : World Scientific
ISBN 13 : 9812382623
Total Pages : 300 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Topological Methods, Variational Methods and Their Applications by : Haim Brzis

Download or read book Topological Methods, Variational Methods and Their Applications written by Haim Brzis and published by World Scientific. This book was released on 2003 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

Flat Level Set Regularity of $p$-Laplace Phase Transitions

Author : Enrico Valdinoci
Publisher : American Mathematical Soc.
ISBN 13 : 0821839101
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Flat Level Set Regularity of $p$-Laplace Phase Transitions by : Enrico Valdinoci

Download or read book Flat Level Set Regularity of $p$-Laplace Phase Transitions written by Enrico Valdinoci and published by American Mathematical Soc.. This book was released on 2006 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers. In particular, if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for $p=2$ follows.