46146 - Nonlinear Analysis

Academic Year 2024/2025

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)

Learning outcomes

At the end of the course the student knows some aspects of the theory of non linear systems with particular emphasis on PDEs and is able to recognize the principal peculiarities of nonlinearity and similarities or difference with linear analysis.

Course contents

The course treats the basic ideas and tecniques on minimax methods in the variational theory of critical points. The main contents are:

- Palais-Smale compactness condition
- Deformation lemma
- Mountain pass theorem
- Applications to elliptic PDEs
- Minimax principle
- Properties of linking method
- Applications to Hamiltonian systems

 

However, the course will be taught in Italian: see the italian version for the detailed program.

46146 - ANALISI NON LINEARE

Readings/Bibliography

- M.Struwe, Variational Methods; Springer
- A.Ambrosetti, A.Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems; Cambridge University Press
- P.H.Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations; AMS-CBMS

Teaching methods

Lectures in classroom.

Assessment methods

Final oral exam.

Teaching tools

Additional material can be found on Virtuale.

Office hours

See the website of Vittorio Martino