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arXiv · 2609.24179

Structure of radial solutions to a Hénon type equation with exponential nonlinearity on the hyperbolic space

Yahui Jiang·Xianmei Zhou
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Abstract

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.

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Yahui Jiang, Xianmei Zhou. 2026-09-21. Structure of radial solutions to a Hénon type equation with exponential nonlinearity on the hyperbolic space. https://arxiv.org/abs/2609.24179

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