Angela Pistoia Universitá di Roma 1 (Italy)
On the existence of sign changing solutions for the Bahri-Coron problem
Let Ω be a bounded smooth domain in RN, N ≥ 3 and p = N+2
N-2. We are interested in existence and multiplicity
of sign changing solutions to the slightly subcritical problem
to the Bahri-Coron’s problem
Ωε = 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 (). When Ω is symmetric and contains the
origin, we construct sign changing solutions to problems (1) () and (2) () with multiple blow
up at the origin. These solutions have, as ε goes to zero, more and more annular-shaped nodal
- 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 Bahri-Coron’s problem in pierced domains,
- 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).