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<p>In this article, we study the solvability of a class of fractional Kirchhoff-Choquard double phase problem with singular nonlinearities. Based on appropriate assumptions, we derive an existence result of two weak solutions via the fibering method in form of the Nehari manifold. Some basic inequality techniques such as Hardy-Littlewood-Sobolev inequality are applied to deal with Choquard nonlinearity. In order to handle the weight function in fractional double phase operators with Dirichlet boundary conditions, the corresponding new fractional Musielak-Sobolev space is established, and some relevant properties are also obtained.</p>

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A new fractional Musielak-Sobolev space and Choquard-Kirchhoff double phase problem with singular nonlinearities

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Yu Cheng,
  • Zhanbing Bai

摘要

In this article, we study the solvability of a class of fractional Kirchhoff-Choquard double phase problem with singular nonlinearities. Based on appropriate assumptions, we derive an existence result of two weak solutions via the fibering method in form of the Nehari manifold. Some basic inequality techniques such as Hardy-Littlewood-Sobolev inequality are applied to deal with Choquard nonlinearity. In order to handle the weight function in fractional double phase operators with Dirichlet boundary conditions, the corresponding new fractional Musielak-Sobolev space is established, and some relevant properties are also obtained.