2019/03/05 by Massimo Grossi, Gabriele Mancini, Grossi, Massimo +5
Computer Science · Mathematics · #35B33 #35B44 #35J20 #35J61 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #msc:35B33 #msc:35B44 #msc:35J20 #msc:35J61
paper · pdf · doi:10.48550/arxiv.1903.02060
arxiv created 2019/03/05 · openalex publication_date 2019/03/05 · arxiv updated 2019/03/07 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In this work we study the existence of nodal solutions for the problem -Δu = λu eu2+|u|p in Ω, u = 0 on ∂ Ω, where Ω⊆ \mathbb R2 is a bounded smooth domain and p→ 1+. If Ω is ball, it is known that the case p=1 defines a critical threshold between the existence and the non-existence of radially symmetric sign-changing solutions. In this work we construct a blowing-up family of nodal solutions to such problem as p→ 1+, when Ω is an arbitrary domain and λ is small enough. As far as we know, this is the first construction of sign-changing solutions for a Moser-Trudinger critical equation on a non-symmetric domain.