Stability of Semilinear Elliptic Equations with Hénon Type Weighted Exponential Nonlinearity in Hyperbolic Space

Xia Huang; Chun Yi Zhao

doi:10.1007/s10255-025-0040-7

Stability of Semilinear Elliptic Equations with Hénon Type Weighted Exponential Nonlinearity in Hyperbolic Space

Xia Huang
, Chun Yi Zhao^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

This study delves into the Hénon-type weighted elliptic equation, given by -Δ_gu = (sinh r)^α_e^u, within the context of hyperbolic space ℍⁿ, where α > 0 and n > 2. Our research reveals notable distinctions in the stability of solutions when compared to the Euclidean case.

Original language	English
Pages (from-to)	95-104
Number of pages	10
Journal	Acta Mathematicae Applicatae Sinica
Volume	42
Issue number	1
DOIs	https://doi.org/10.1007/s10255-025-0040-7
State	Published - Jan 2026

Keywords

35B35
Hénon type weighted exponential nonlinearity
hyperbolic space
stable solutions

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title = "Stability of Semilinear Elliptic Equations with H{\'e}non Type Weighted Exponential Nonlinearity in Hyperbolic Space",

abstract = "This study delves into the H{\'e}non-type weighted elliptic equation, given by -Δgu = (sinh r)αeu, within the context of hyperbolic space ℍn, where α > 0 and n > 2. Our research reveals notable distinctions in the stability of solutions when compared to the Euclidean case.",

keywords = "35B35, H{\'e}non type weighted exponential nonlinearity, hyperbolic space, stable solutions",

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AU - Zhao, Chun Yi

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PY - 2026/1

Y1 - 2026/1

N2 - This study delves into the Hénon-type weighted elliptic equation, given by -Δgu = (sinh r)αeu, within the context of hyperbolic space ℍn, where α > 0 and n > 2. Our research reveals notable distinctions in the stability of solutions when compared to the Euclidean case.

AB - This study delves into the Hénon-type weighted elliptic equation, given by -Δgu = (sinh r)αeu, within the context of hyperbolic space ℍn, where α > 0 and n > 2. Our research reveals notable distinctions in the stability of solutions when compared to the Euclidean case.

KW - 35B35

KW - Hénon type weighted exponential nonlinearity

KW - hyperbolic space

KW - stable solutions

UR - https://www.scopus.com/pages/publications/105006676226

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JF - Acta Mathematicae Applicatae Sinica

IS - 1

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Stability of Semilinear Elliptic Equations with Hénon Type Weighted Exponential Nonlinearity in Hyperbolic Space

Abstract

Keywords

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