Nonexistence results for biharmonic boundary value problems with supercritical growth

We consider here the following biharmonic equations: Δ² u = f(u) & in Ω u = ∇ u = 0 & on ∂Ω, . Δ² u = f(u) & Ω u = Δ u = 0 & on ∂Ω. We prove that for N < 6 (resp. for N < 10), there exist topologically nontrivial, smooth bounded domains Ω ⊂ (N) and suitable supercritical nonlinearities f such that there does not exist any nontrivial solution. These results are similar to some of those proved by Passaseo (see [11, 12]) for the Laplacian case.