Perturbation Methods and Semilinear Elliptic Problems on Rn [electronic resource] / by Antonio Ambrosetti, Andrea Malchiodi.

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 Schrȵdinger Equations -- Singularly Perturbed Neumann Problems -- Concentration at Spheres for Radial Problems.

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