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<p>In this work, we examine whether nonnegative solutions exist for a Kirchhoff-type issue that is driven by a fractional <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3291_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">d</mi> <mrow> <mo>(</mo> <mi mathvariant="normal">z</mi> <mo>,</mo> <mo>.</mo> <mo>)</mo> </mrow> <mo>−</mo> </math></EquationSource> <EquationSource Format="TEX">$\mathrm{d}\left (\mathrm{z},.\right )-$</EquationSource> </InlineEquation> Laplacian operator, where d is a continuous positive function. We establish the existence of their nonnegative solutions combined with the theory of fractional Sobolev spaces with variable exponents by using approximation methods.</p>

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Kirchhoff-type problems with the non-local fractional \(\mathrm{d}(\mathrm{z},.)\)-Laplacian operator

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月27日

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  • Ahlem Yahiaoui,
  • Med-Salem Rezaoui,
  • Omar Djidel,
  • Rafik Guefaifia,
  • Salah Boulaaras

摘要

In this work, we examine whether nonnegative solutions exist for a Kirchhoff-type issue that is driven by a fractional d ( z , . ) − $\mathrm{d}\left (\mathrm{z},.\right )-$ Laplacian operator, where d is a continuous positive function. We establish the existence of their nonnegative solutions combined with the theory of fractional Sobolev spaces with variable exponents by using approximation methods.