发表机构
East China Normal University; Zhejiang Normal University（华东师范大学; 浙江师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过将双曲径向方程转化为加权欧几里得方程，利用欧几里得分离结果，完整分类了双曲空间上指数非线性Hénon型方程径向解的结构，并肯定了Huang和Zhao的开放问题。
AI 中文摘要
本文研究了双曲空间上具有指数非线性项的Hénon型方程径向解的分离性与稳定性性质。通过将径向双曲方程转化为带权欧几里得方程，并应用欧几里得空间中成熟的分离结果，我们在$n\ge2$且$\alpha>-2$的完整参数范围内，对径向解的结构进行了分类或建立了尖锐的备选结论。我们还对Huang和Zhao最近提出的开放问题给出了肯定回答。
英文摘要
In this paper, we study the separation and stability properties of radial solutions to a Hénon-type equation with exponential nonlinearity on the hyperbolic space. By transforming the radial hyperbolic equation into a weighted Euclidean equation and applying well-established separation results in Euclidean space, we classify the solution structures or establish sharp alternatives for radial solutions throughout the full range $n\ge2$ and $α>-2$. We also give an affirmative answer to the open question recently posed by Huang and Zhao.
Comments11 pages
