2019/04/04 by Gabriele Cora, Cora, Gabriele, Alessandro Iacopetti +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1904.02738
openalex publication_date 2019/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the asymptotic and qualitative properties of least energy radial\nsign-changing solutions to fractional semilinear elliptic problems of the form\n\
begincases (-
Delta)s u = |u|2^*s-2-
varepsilonu amp;
textin BR,
ν = 0 amp;
textin
mathbbRn
setminus BR,
endcases where s \∈\n(0,1), (-\Δ)s is the s-Laplacian, BR is a ball of \ℝn,\n2^*s := \(2n)/(n-2s) is the critical Sobolev exponent and \ε>0\nis a small parameter. We prove that such solutions have the limit profile of a\n"tower of bubbles", as \ε \→ 0+, i.e. the positive and negative\nparts concentrate at the same point with different concentration speeds.\nMoreover, we provide information about the nodal set of these solutions.\n