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<p>In this paper, we establish a Hardy-Sobolev inequality with an optimal constant in the critical range for the fractional Sobolev spaces on compact Riemannian manifolds. Furthermore, we prove the existence of a nontrivial solution for a nonlinear nonlocal equation involving the fractional <i>p</i>-Laplacian operator and a critical Hardy-Sobolev nonlinearity.</p>

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Hardy-Sobolev Inequality and Existence of Solutions For Fractional p-Laplacian Equation with Critical Hardy-Sobolev Nonlinearity on Compact Riemannian Manifolds

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Shengbing Deng,
  • Minli Liao

摘要

In this paper, we establish a Hardy-Sobolev inequality with an optimal constant in the critical range for the fractional Sobolev spaces on compact Riemannian manifolds. Furthermore, we prove the existence of a nontrivial solution for a nonlinear nonlocal equation involving the fractional p-Laplacian operator and a critical Hardy-Sobolev nonlinearity.