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<p>In this paper, we focus on the study of the fractional Sobolev spaces with variable exponents and the corresponding <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3284_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">\(p(x,.)-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mo>.</mo> <mo stretchy="false">)</mo> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation> Laplacian operator under Neumann boundary conditions. We prove some basic proprieties of the functional spaces and, in order to unsure the applicability, we prove the existence of solutions for a fractional elliptic system using the Mountain Pass Theorem.</p>

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On a class of fractional elliptic systems with variable exponents under Neumann boundary conditions

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Elhoussine Azroul,
  • Athmane Boumazourh,
  • Houria El-Yahyaoui

摘要

In this paper, we focus on the study of the fractional Sobolev spaces with variable exponents and the corresponding \(p(x,.)-\) p ( x , . ) - Laplacian operator under Neumann boundary conditions. We prove some basic proprieties of the functional spaces and, in order to unsure the applicability, we prove the existence of solutions for a fractional elliptic system using the Mountain Pass Theorem.