SEMINAR @ SISSSA, prof. Berti course: II section 23-27 April

[Barbara Corzani]

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FUNCTIONAL ANALYSIS SECTOR'S ACTIVITIES
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COURSE: II SECTION

Prof. 
Massimiliano Berti
(Università di Napoli)

Title:
"Classical and hard Implicit function theorems"


Mon   23 April 2007  @  11.00-12.30 
Tue    24 April 2007  @  11.00-12.30  
                              @  14.30-16.00
Thu.   26 April 2007 @   11.00-12.30
Fri      27 April 2007 @   11.00-12.30

SISSA - Main Building - ground floor - room B

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I part: the classical implicit function theorem

1) The classical implicit function theorems in Banach spaces and some  applications to bifurcation theory
(for example Rabinowitz existence result of periodic solutions of  wave equations)
2) Examples of cases where the classical theorem fails because of  "loss of derivatives"

II part: the hard implicit function theorem

1) The Newton method
2) The Nash-Moser implicit function theorem  in scales of analytic  Banach spaces (with an application to Siegel conjugacy problem)
  - Seminar of P. Baldi where, using these analytic techniques,  existence of periodic solutions for the wave and the Kirchhoff  equations is proved
3) The Nash-Moser implicit function theorem in scales of Sobolev  Banach spaces