Description
- basic review of calculus in Banach spaces
- free and constrained critical points
- the Palais-Smale condition and the deformation lemma
- the Mountain-Pass theorem and other variational schemes
- Lusternik-Schnirelman category
- Krasnoselski genus
- problems with lack of compactness (time permitting)
The exam will consist of a written part (about 1 hour and a half), and an oral part.
References:
- Ambrosetti, Antonio; Malchiodi, Andrea Nonlinear analysis and semilinear elliptic problems.
Cambridge Studies in Advanced
Mathematics, 104. Cambridge University Press, Cambridge, 2007.
- Struwe, Michael Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems.
Springer-Verlag, Berlin, 2008.