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<p>In this paper, we consider a variable-order fractional <i>p</i>(<i>x</i>)-Laplacian problem of Kirchhoff-type depending on a real parameter. By variational arguments and using the monotone operator theory in a suitable variable-exponent fractional Sobolev space, we provide sufficient conditions that ensure existence and uniqueness of solutions. Furthermore, many properties of the solution are obtained.</p>

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Existence and uniqueness result for a variable-order fractional p(x)-Laplacian problem of Kirchhoff-type

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Mohammed Massar

摘要

In this paper, we consider a variable-order fractional p(x)-Laplacian problem of Kirchhoff-type depending on a real parameter. By variational arguments and using the monotone operator theory in a suitable variable-exponent fractional Sobolev space, we provide sufficient conditions that ensure existence and uniqueness of solutions. Furthermore, many properties of the solution are obtained.