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<p>This study delves into the Hénon-type weighted elliptic equation, given by -Δ<sub><i>g</i></sub><i>u</i> = (sinh <i>r</i>)<sup><i>α</i></sup><sub><i>e</i></sub><sup><i>u</i></sup>, within the context of hyperbolic space ℍ<sup><i>n</i></sup>, where <i>α</i> &gt; 0 and <i>n</i> &gt; 2. Our research reveals notable distinctions in the stability of solutions when compared to the Euclidean case.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Xia Huang,
  • Chun-yi Zhao

摘要

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.