Angela Pistoia Universitá di Roma 1 (Italy)
On the existence of sign changing solutions for the BahriCoron problem
Let Ω be a bounded smooth domain in R^{N}, N ≥ 3 and p = N+2
N2. We are interested in existence and multiplicity
of sign changing solutions to the slightly subcritical problem
and
to the BahriCoron’s problem
when
Ω_{ε} = Ω \B(0,ε). In both cases ε is a small positive parameter. We prove that, problem (1) has at least N pairs
of solutions which change sign exactly once. Moreover, the nodal surface of these solutions intersects the
boundary of Ω, provided some suitable conditions are satisfied ([1]). When Ω is symmetric and contains the
origin, we construct sign changing solutions to problems (1) ([3]) and (2) ([2]) with multiple blow
up at the origin. These solutions have, as ε goes to zero, more and more annularshaped nodal
domains.
 T. Bartsch, A.M. Micheletti, A. Pistoia, On the existence and the profile of nodal solutions
of elliptic equations involving critical growth, Calc. Var. Partial Differential Equations (to appear).
 M. Musso, A. Pistoia, Sign changing solutions to BahriCoron’s problem in pierced domains,
(preprint).
 A. Pistoia, T. Weth, Sign changing bubble tower solutions in a slightly subcritical semilinear
Dirichlet problem, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear).
