Perturbation Methods and Semilinear Elliptic Problems on R n

✍ Scribed by Antonio Ambrosetti, Andrea Malchiodi (auth.)

• Publisher: Birkhäuser Basel
• Year: 2006
• Tongue: English
• Leaves: 187
• Series: Progress in Mathematics 240
• Edition: 1
• Category: Library

✦ Synopsis

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 Schrödinger equations, and singularly perturbed
elliptic problems in domains. These topics are presented in a systematic and
unified way.

✦ Table of Contents

Examples and Motivations....Pages 1-11
Pertubation in Critical Point Theory....Pages 13-33
Bifurcation from the Essential Spectrum....Pages 35-44
Elliptic Problems on ℝ n with Subcritical Growth....Pages 45-58
Elliptic Problems with Critical Exponent....Pages 59-71
The Yamabe Problem....Pages 73-100
Other Problems in Conformal Geometry....Pages 101-113
Nonlinear Schrödinger Equations....Pages 115-133
Singularly Perturbed Neumann Problems....Pages 135-149
Concentration at Spheres for Radial Problems....Pages 151-172

✦ Subjects

Numerical Analysis; Partial Differential Equations; Functional Analysis