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<p>We prove new multiplicity results for some nonlocal critical growth elliptic equations in homogeneous fractional Sobolev spaces. The proofs are based on an abstract critical point theorem based on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb Z_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-cohomological index and on a novel regularity result for fractional <i>p</i>-Laplacian equations as well as on some compact embeddings.</p>

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Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Siegfried Carl,
  • Kanishka Perera,
  • Hossein Tehrani

摘要

We prove new multiplicity results for some nonlocal critical growth elliptic equations in homogeneous fractional Sobolev spaces. The proofs are based on an abstract critical point theorem based on the \(\mathbb Z_2\) Z 2 -cohomological index and on a novel regularity result for fractional p-Laplacian equations as well as on some compact embeddings.