Mathematics

 Program:

• 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 (time permitting)
• Krasnoselski genus (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.