Massimo Grossi

Existence results for the Brezis-Nirenberg Problem in the supercritical case

Let us consider the equation -Δu + a(|x|)u = u^p in the unit ball of Rⁿ, n ≥ 3. We show, under suitable assumptions on a, the existence of positive solutions with zero Dirichlet boundary conditions if the exponent p is large enough. The proof of this result relies on the existence of a ‘limit problem’ as p →∞. This is a joint paper with Angela Pistoia.