2005 – Non linear analysis


organizer Nicolas Macris
office INR 134
phone 38114
email [email protected]
schedule monday 11h – 12h30
location room INR 113


We often seek information on solutions of non-linear differential or integral equations. Non linear analysis combines methods from analysis and topology including fixed point theorems (Brouwer, Schauder), degree theory (Brouwer, Leray-Schauder degree), the Krasnoselskii-Rabinowitz bifurcation theorem. We plan to study a little book which contains an introduction to these topics plus applications:

A Topological Introduction to Non Linear Analysis, by Robert Brown (Birkhauser 1993)
Another set of useful techniques use various perturbation methods. In a second stage we may read pieces of the short book:

Perturbation Techniques for Mathematics, Engineering, Physics, by Richard Bellman (Dover 2004)
Relevant material will be distributed to interested participants. We will meet on a weekly basis for presentations of 1h or 1h30.

Additional reading material

Numerical path following, by Eugene Allgower, Kurt Georg (1994)
Non linear functional analysis, by Gerald Teschl (2005)

Evolving schedule

speaker date topic
Nicolas Macris Oct 24 Nishimori identities
Satish Korada Oct 31 Exact replica symmetric solution of an SK like model
Sanket Dusad Nov 7 Compactness in metric spaces
Sanket Dusad Nov 13 Ascoli-Arzela theorem
Ruediger Urbanke Nov 21 Fixed point theorems: Brouwer and Schauder
Ruediger Urbanke Nov 28 Schauder fixed point theorem and applications
Henry Pfister Dec 5 Fixed points equations with a parameter and GEXIT curves
Vishwambar Rathi Dec 12 Homotopy and Brouwer’s theorem for the disc
Vishwambar Rathi Dec19 Homotopy and Brouwer’s theorem for the disc
break Jan 9 – – –
Harm Cronie Jan 16 Brouwer mapping degree
Harm Cronie Jan23 Brouwer mapping degree
Shrinivas Kudekar Jan 30 Leray Schauder degree
Shrinivas Kudekar Feb 15 (wed 14h15 !) Leray Schauder continued
Shrinivas Kudekar Feb 20 Compact linear operators