- Docente: Vittorio Martino
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Sep 18, 2024 to Dec 12, 2024
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.
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