Università Roma Tre

Calculus in Banach spaces, derivation, Implicit Function Theorem;
Bifurcation theorem, Ljapunov-Schmidt method;
Energy-minimizing solutions, coercivity, lower semi-continuity;
Saddle point solutions, Mountain Pass Theorem;
Topological degree, Linking Theorems;
Ljusternik-Schnirelmann Category, existence of infinitely many solutions.

A. Ambrosetti, A. Malchiodi - "Nonlinear Analysis and Semilinear Elliptic Problem" - Cambridge
P. Rabinowitz - "Minimax methods in critical point theory with application to differential equations" - American Mathematical Society