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<p>The paper addresses the existence of multi-bubble solutions for the well-known Brezis–Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded domain remains an open problem. The goal of the present paper is to resolve this longstanding issue. In particular, we exhibit examples of domains where a large number of multi-bubble solutions exist. Our result can also be seen as the counterpart of the asymptotic analysis carried out by König and Laurin in <i>Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2024</i>.</p>

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Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Angela Pistoia,
  • Giuseppe Mario Rago,
  • Giusi Vaira

摘要

The paper addresses the existence of multi-bubble solutions for the well-known Brezis–Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded domain remains an open problem. The goal of the present paper is to resolve this longstanding issue. In particular, we exhibit examples of domains where a large number of multi-bubble solutions exist. Our result can also be seen as the counterpart of the asymptotic analysis carried out by König and Laurin in Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2024.