![Perturbation Methods and Semilinear Elliptic Problems on R[superscript N] PDF](https://books.google.com/books/content/images/frontcover/-jCIswEACAAJ?fife=w150-h200)
Author: Antonio AmbrosettiPublisher: Birkhauser
ISBN: 9780817673215
Category : Boundary value problems
Languages : en
Pages : 183
Book Description
Perturbation Methods and Semilinear Elliptic Problems on R[superscript N]
![Perturbation Methods and Semilinear Elliptic Problems on R[superscript N] PDF](https://books.google.com/books/content/images/frontcover/-jCIswEACAAJ?fife=w80-h100)
Author: Antonio AmbrosettiPublisher: Birkhauser
ISBN: 9780817673215
Category : Boundary value problems
Languages : en
Pages : 183
Book Description
Perturbation Methods and Semilinear Elliptic Problems on R^n
Author: Antonio AmbrosettiPublisher: Birkhäuser
ISBN: 9783764390860
Category : Mathematics
Languages : en
Pages : 184
Book Description
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^n
Author: Antonio AmbrosettiPublisher: Springer Science & Business Media
ISBN: 3764373962
Category : Mathematics
Languages : en
Pages : 187
Book Description
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
Author: Marino BadialePublisher: Springer Science & Business Media
ISBN: 0857292277
Category : Mathematics
Languages : en
Pages : 204
Book Description
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.
Nonlinear Problems with Lack of Compactness
Author: Giovanni Molica BisciPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110648938
Category : Mathematics
Languages : en
Pages : 191
Book Description
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.
Variational Principles in Mathematical Physics, Geometry, and Economics
Author: Alexandru KristályPublisher: Cambridge University Press
ISBN: 0521117828
Category : Mathematics
Languages : en
Pages : 385
Book Description
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
Author: Yanheng DingPublisher: World Scientific
ISBN: 9814474509
Category : Mathematics
Languages : en
Pages : 177
Book Description
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 $S^n$
Author: Man Chun LeungPublisher: American Mathematical Soc.
ISBN: 0821853376
Category : Mathematics
Languages : en
Pages : 112
Book Description
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
Author: Yisong YangPublisher: World Scientific
ISBN: 9814289302
Category : Science
Languages : en
Pages : 371
Book Description
Gun Shy
Representation Theory and Automorphic Forms
Author: Toshiyuki KobayashiPublisher: Springer Science & Business Media
ISBN: 0817646469
Category : Mathematics
Languages : en
Pages : 220
Book Description
This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.