Isolated singularities for elliptic equations with Hardy operator and source nonlinearity

2017/06/06 by Huyuan Chen, Feng Zhou, Chen, Huyuan +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1706.01793

openalex publication_date 2017/06/06 · openalex created_date 2017/06/15 · openalex updated_date 2026/07/28

Abstract

In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials -Δu+\fracμ|x|² u=u^p \rm in Ω∖\0\, u=0 \rm on ∂Ω. We classify the isolated singularities and obtain the existence, the stability of positive solutions of (\ref0). Our results are based on the study of nonhomogeneous Hardy problem in a new distributional sense.

Citations

• A nonlinear elliptic Pde with the inverse square potential
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• On nonhomogeneous elliptic equations with the Hardy-Leray potentials

Cited by

• Isolated singularities for elliptic equations with convolution terms in a punctured ball

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