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<p>We study a class of nonlocal Kirchhoff-type equations driven by a fractional integro-differential operator acting in fractional Musielak–Sobolev spaces. The equation is considered with homogeneous Dirichlet boundary conditions. The model combines three different sources of nonlocality: a fractional operator, a Kirchhoff coefficient depending on a nonlocal energy, and a Musielak-type modular depending on the points of the domain. We cast the problem in a variational setting and apply a three critical points theorem due to Ricceri. Under suitable assumptions on the Kirchhoff function and on the nonlinear terms, we prove the existence of at least three weak solutions. The result extends previous multiplicity theorems for Kirchhoff-type and fractional problems to a more general framework with nonstandard growth.</p>

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Multiple weak solutions for a fractional kirchhoff-type problem in Musielak–Sobolev spaces

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Mohammed Allou,
  • Elhoussine Azroul,
  • Mohammed Srati

摘要

We study a class of nonlocal Kirchhoff-type equations driven by a fractional integro-differential operator acting in fractional Musielak–Sobolev spaces. The equation is considered with homogeneous Dirichlet boundary conditions. The model combines three different sources of nonlocality: a fractional operator, a Kirchhoff coefficient depending on a nonlocal energy, and a Musielak-type modular depending on the points of the domain. We cast the problem in a variational setting and apply a three critical points theorem due to Ricceri. Under suitable assumptions on the Kirchhoff function and on the nonlinear terms, we prove the existence of at least three weak solutions. The result extends previous multiplicity theorems for Kirchhoff-type and fractional problems to a more general framework with nonstandard growth.