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Structure of radial solutions to a Hénon type equation with exponential nonlinearity on the hyperbolic space
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≥2 and α>−2. We also give an affirmative answer to the open question recently posed by Huang and Zhao.
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BibTeX
@misc{jiang2026structure,
title = {{Structure of radial solutions to a Hénon type equation with exponential nonlinearity on the hyperbolic space}},
author = {Yahui Jiang and Xianmei Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24179},
eprint = {2609.24179},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24179},
}
RIS
TY - UNPB
TI - Structure of radial solutions to a Hénon type equation with exponential nonlinearity on the hyperbolic space
AU - Yahui Jiang
AU - Xianmei Zhou
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24179
UR - https://arxiv.org/abs/2609.24179
AB - 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≥2 and α>−2. We also give an affirmative answer to the open question recently posed by Huang and Zhao.
ER -