He is known for his basic work on topological methods in the calculus of variations.

These provide tools aimed at establishing the existence of solutions to variational problems when classical direct methods of the calculus of variations cannot be applied.

In particular, the so-called mountain pass theorem he established with Paul Rabinowitz is nowadays a classical tool in the context of nonlinear analysis problems.

Jointly with Andrea Malchiodi, Ambrosetti has been awarded the 2005 edition of the Ferran Sunyer i Balaguer prize.

[4] In 1983 he has been invited speaker at the International Congress of Mathematicians and he was fellow of the Accedemia Nazionale dei Lincei.