Sign-changing bubbling solutions for an exponential nonlinearity in ℝ²

2024/03/12 by Yibin Zhang, Zhang, Yibin
Mathematics · #Advanced Mathematical Physics Problems #math.AP

paper · pdf · doi:10.48550/arxiv.2403.07641

openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Very differently from those perturbative techniques of Deng-Musso in [26], we use the assumption of a C¹-stable critical point to construct positive or sign-changing solutions with arbitrary m isolated bubbles to the boundary value problem -Δu=λu|u|^p-2e^|u|p under homogeneous Dirichlet boundary condition in a bounded, smooth planar domain Ω, when 00 is a small but free parameter. We build a vanishing identity of first order and an identity of second order to prove that for any 0

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