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

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
Journal	Acta Mathematicae Applicatae Sinica
DOIs	https://doi.org/10.1007/s10255-025-0040-7
State	Accepted/In press - 2025

Keywords

35B35
Hénon type weighted exponential nonlinearity
hyperbolic space
stable solutions

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10.1007/s10255-025-0040-7

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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",

author = "Xia Huang and Zhao, \{Chun Yi\}",

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year = "2025",

doi = "10.1007/s10255-025-0040-7",

language = "英语",

journal = "Acta Mathematicae Applicatae Sinica",

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AU - Huang, Xia

AU - Zhao, Chun Yi

N1 - Publisher Copyright: © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2025.

PY - 2025

Y1 - 2025

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

U2 - 10.1007/s10255-025-0040-7

DO - 10.1007/s10255-025-0040-7

M3 - 文章

AN - SCOPUS:105006676226

SN - 0168-9673

JO - Acta Mathematicae Applicatae Sinica

JF - Acta Mathematicae Applicatae Sinica

ER -

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

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Keywords

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