A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions*Research partially supported by: INDAM-GNAMPA. (14th October 2021)

• Record Type: Journal Article
• Authors: Amadori, A L; Gladiali, F; Grossi, M; Pistoia, A; Vaira, G
• Is Part Of: Nonlinearity. Volume 34:Number 11(2021)
• Page Start: 8055
• Page End: 8093
• Publication Date: 2021-10-14
• Subjects: Brezis–Nirenberg problem -- asymptotic analysis -- Green function; 35A09 -- 35B33 -- 35B40 -- 35J15; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac2a4e
• Languages: English
• ISSNs: 0951-7715

Abstract

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 ].