Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem

2015/02/05 by Monica Musso, Juncheng Wei, Musso, Monica +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1502.01674

openalex publication_date 2015/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be a bounded domain in \Rⁿ, n≥ 3 with smooth boundary ∂Ω and a small hole. We give the first example of sign-changing \it bubbling solutions to the nonlinear elliptic problem -Δu=|u|^n+2\over n-2 +\ve -1 u in Ω, u=0 on ∂ Ω, where \ve is a small positive parameter. The basic cell in the construction is the sign-changing nodal solution to the critical Yamabe problem -Δw = |w|^(4)/(n-2) w, w ∈ \mathcal D^1,2 (\Rⁿ) which has large number (3n) of kernels.

Citations

• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

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