A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions*Research partially supported by: INDAM-GNAMPA. (14th October 2021) - Amadori, A L; Gladiali, F; Grossi, M; Pistoia, A; Vaira, G
Abstract: In this paper we consider nodal radial solutions of the problem − Δ u = | u | 2 * − 2 u + λ u in B, u = 0 on ∂ B where 2 * = 2 N N − 2 with 3 ⩽ N ⩽ 6 and B is the unit ball of IR N . We compute the asymptotics of the solution u as well as ‖ u ‖∞, its first zero and other relevant quantities as λ goes to a critical value λ ¯ . Also the sign of λ − λ ¯ is established in all cases. This completes an analogous analysis for N ⩾ 7 given in [12 ].