Ricerc@Sapienza

In this paper we consider sign-changing radial solutions u ε
to the problem

−∆u = λue^{u^2} +|u|^{1+ε} in B,
u =0 on ∂B,
and we study their asymptotic behaviour as ε & 0.
We show that when u ε = u ε (r) has k interior zeros, it exhibits a multiple
blow–up behaviour in the first k nodal sets while it converges to the least
energy solution of the problem with ε = 0 in the (k + 1)–th one. We
also prove that in each concentration set, with an appropriate scaling,
u ε converges to the solution of the classical Liouville problem in R 2 .