A Morse Lemma for degenerate critical points of solutions of nonlinear equations in $\R^2$

Abstract

In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies -Δu=f(u) in B_1, where B_1 is the unit ball of R^2 and f is a smooth nonlinearity. Other results on the nondegeneracy of the critical points and the shape of the level sets are proved.