Perturbation Methods And Semilinear Elliptic Problems On R N
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Perturbation Methods And Semilinear Elliptic Problems On R N
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Author : Antonio Ambrosetti
language : en
Publisher: Birkhäuser
Release Date : 2009-09-03
Perturbation Methods And Semilinear Elliptic Problems On R N written by Antonio Ambrosetti and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Mathematics categories.
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.
Perturbation Methods And Semilinear Elliptic Problems On R Superscript N
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Author : Antonio Ambrosetti
language : en
Publisher: Birkhauser
Release Date : 2006
Perturbation Methods And Semilinear Elliptic Problems On R Superscript N written by Antonio Ambrosetti and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Boundary value problems categories.
Perturbation Methods And Semilinear Elliptic Problems On R N
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Author : Antonio Ambrosetti
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
Perturbation Methods And Semilinear Elliptic Problems On R N written by Antonio Ambrosetti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-21 with Mathematics categories.
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.
Semilinear Elliptic Equations For Beginners
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Author : Marino Badiale
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-07
Semilinear Elliptic Equations For Beginners written by Marino Badiale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-07 with Mathematics categories.
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 Principles In Mathematical Physics Geometry And Economics
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Author : Alexandru Kristály
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-19
Variational Principles In Mathematical Physics Geometry And Economics written by Alexandru Kristály and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Mathematics categories.
A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.
Variational Methods For Strongly Indefinite Problems
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Author : Yanheng Ding
language : en
Publisher: World Scientific
Release Date : 2007-07-30
Variational Methods For Strongly Indefinite Problems written by Yanheng Ding and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-30 with Mathematics categories.
This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.
Supported Blow Up And Prescribed Scalar Curvature On S N
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Author : Man Chun Leung
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Supported Blow Up And Prescribed Scalar Curvature On S N written by Man Chun Leung and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The author expounds the notion of supported blow-up and applies it to study the renowned Nirenberg/Kazdan-Warner problem on $S^n$. When $n \ge 5$ and under some mild conditions, he shows that blow-up at a point with positive definite Hessian has to be a supported isolated blow-up, which, when combined with a uniform volume bound, is a removable singularity. A new asymmetric condition is introduced to exclude single simple blow-up. These enable the author to obtain a general existence theorem for $n \ge 5$ with rather natural condition.
Perspectives In Mathematical Sciences
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Author : Yisong Yang
language : en
Publisher: World Scientific
Release Date : 2010
Perspectives In Mathematical Sciences written by Yisong Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
Gun Shy
Nonlinear Problems With Lack Of Compactness
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Author : Giovanni Molica Bisci
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-02-08
Nonlinear Problems With Lack Of Compactness written by Giovanni Molica Bisci and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.
This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
Analytical And Numerical Aspects Of Partial Differential Equations
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Author : Etienne Emmrich
language : en
Publisher: Walter de Gruyter
Release Date : 2009
Analytical And Numerical Aspects Of Partial Differential Equations written by Etienne Emmrich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.