Ricerc@Sapienza

In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies - Δ u = f (u) in B1, where u ∈ C2 (B1), B1 is the unit ball of R2 and f is a smooth nonlinearity. Other results on the nondegeneracy of the critical points and the shape of the level sets are proved.