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<p>We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that the potential of the linear operator touches a critical potential at the singular point. This condition is sharp as shown by the first author in [<CitationRef CitationID="CR1">1</CitationRef>].</p>

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Ground-State Blowing-up Solutions for a Hardy-Sobolev Equation on a Manifold

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Hussein Cheikh Ali,
  • Frédéric Robert

摘要

We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that the potential of the linear operator touches a critical potential at the singular point. This condition is sharp as shown by the first author in [1].