Perturbative theory and Lyapunov-Schmidt reduction

Period of duration of course
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Course info
Number of course hours
20
Number of hours of lecturers of reference
20
Number of hours of supplementary teaching
0
CFU 3
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Modalità esame

Oral exam and seminars

Lecturer

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Prerequisiti

Functonal Analysis, Elliptic regularity theory. It might be useful some knowledge of topological degree theory. 

Programma

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

Obiettivi formativi

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.

Riferimenti bibliografici

A.Ambrosetti - A.Malchiodi: Perturbation Methods and Semilinear Elliptic Problems on R^n, Birhkäuser, 2006.