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Birkhäuser - Birkhäuser Mathematics | Perturbation Methods and Semilinear Elliptic Problems on R^n

Perturbation Methods and Semilinear Elliptic Problems on R^n

Series: Progress in Mathematics, Vol. 240

Ambrosetti, Antonio, Malchiodi, Andrea

2006, XII, 184 p.

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  • About this book

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.

Content Level » Research

Keywords » Partial differential equations - Perturbation - Semilinear elliptic problems - compactness - differential equation - equation - geometry - partial differential equation

Related subjects » Birkhäuser Mathematics

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