Perturbative theory and Lyapunov-Schmidt reduction
Period of duration of course
Functonal Analysis, Elliptic regularity theory. It might be useful some knowledge of topological degree theory.
Introduction and motivations
Perturbative critical point theory
Spectral theory for critical and subcritical problems
Semiclassical nonlinear Schroedinger equation
Problems in conformal geometry
Concentration on sets of positive dimension
The purpose of the course is to describe techniques for reducing a certain class of PDEs to a finite-dimensional problem, or to a simpler infinite-dimensional problem. An abstract method of reduction, which is very flexible, will be shown, and we will then move on to applications in relevant problems.
A.Ambrosetti - A.Malchiodi: Perturbation Methods and Semilinear Elliptic Problems on R^n, Birhkäuser, 2006.