A positive solution of the elliptic equation on a starshaped domain with boundary singularities

2025/04/22 by Zhi-Yun Tang, Xianhua Tang, Tang, Zhi-Yun +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2504.16280

openalex publication_date 2025/04/22 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We consider the elliptic equation with boundary singularities \begincases -Δu=-λ|x|^-s₁|u|^p-2u+|x|^-s₂|u|^q-2u amp;\text in \varOmega , u(x)=0 amp;\text on ∂ \varOmega , \endcases where 0≤ s₁ < s₂ < 2, 2q>(2-s₂)/(2-s₁)p+(2s₂-2s₁)/(2-s₁). We also discuss the asymptotic behavior of the positive solution and find a new class of blow-up points by blowing up analysis. These blow-up points are on the boundary of the domain, which are not similar with the usual.

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