Perturbation methods and semilinear elliptic problems on Rn
This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used...
| Main Author: | Ambrosetti, A. |
|---|---|
| Other Authors: | Malchiodi, Andrea., SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Basel :
Birkhauser,
2006.
Basel : 2006. |
| Physical Description: |
1 online resource. |
| Series: |
Progress in mathematics ;
v. 240. |
| Subjects: |
| Summary: |
This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used in general. For these problems, a more specific approach that takes advantage of such a perturbative setting seems to be the most appropriate. The first part of the book is devoted to these abstract tools, which provide a unified frame for several applications, often considered different in nature. Such applications are discussed in the second part, and include semilinear elliptic problems on Rn, bifurcation from the essential spectrum, the prescribed scalar curvature problem, nonlinear Schrodinger equations, and singularly perturbed elliptic problems in domains. These topics are presented in a systematic and unified way. |
|---|---|
| Item Description: |
Examples and Motivations -- Pertubation in Critical Point Theory -- Bifurcation from the Essential Spectrum -- Elliptic Problems on?n with Subcritical Growth -- Elliptic Problems with Critical Exponent -- The Yamabe Problem -- Other Problems in Conformal Geometry -- Nonlinear Schrödinger Equations -- Singularly Perturbed Neumann Problems -- Concentration at Spheres for Radial Problems. This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used in general. For these problems, a more specific approach that takes advantage of such a perturbative setting seems to be the most appropriate. The first part of the book is devoted to these abstract tools, which provide a unified frame for several applications, often considered different in nature. Such applications are discussed in the second part, and include semilinear elliptic problems on Rn, bifurcation from the essential spectrum, the prescribed scalar curvature problem, nonlinear Schrodinger equations, and singularly perturbed elliptic problems in domains. These topics are presented in a systematic and unified way. English. Includes bibliographical references (pages 173-180) and index. |
| Physical Description: |
1 online resource. |
| Bibliography: |
Includes bibliographical references (pages 173-180) and index. |
| ISBN: |
9783764373962 3764373962 3764373210 9783764373214 1280608854 9781280608858 6610608857 9786610608850 |