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<p>In this paper, we study the partial differential equation in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2025_727_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^{N}\)</EquationSource> </InlineEquation> involving multiple Hardy-Sobolev critical exponents. By using some interpolation inequalities, the Pohozaev identity, and an approximating problem, we prove the existence of a positive ground state solution and the regularity of the least-energy solution.</p>

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p-Laplacian Problem with Multiple Hardy-Sobolev Critical Exponents in \(\mathbb {R}^N\)

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Khalid Bouabid,
  • Rachid Echarghaoui

摘要

In this paper, we study the partial differential equation in \(\mathbb {R}^{N}\) involving multiple Hardy-Sobolev critical exponents. By using some interpolation inequalities, the Pohozaev identity, and an approximating problem, we prove the existence of a positive ground state solution and the regularity of the least-energy solution.