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<p>In this paper, we study the existence and multiplicity of solutions for a class of fractional <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_433_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="119" /> </InlineMediaObject> <EquationSource Format="TEX">\((p_{1}(x,\cdot ),p_{2}(x,\cdot ))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian problems with Dirichlet boundary conditions. Working within the framework of fractional Sobolev spaces with variable exponents, we apply the three critical points theorem as our key analytical tool to establish our main results. Under appropriate assumptions, we prove the existence of at least three distinct solutions for the considered problem.</p>

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Multiple solutions for anisotropic nonlocal problems with variable exponents

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月25日

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  • Elhoussine Azroul,
  • Nezha Kamali,
  • Maria Alessandra Ragusa,
  • Mohammed Shimi

摘要

In this paper, we study the existence and multiplicity of solutions for a class of fractional \((p_{1}(x,\cdot ),p_{2}(x,\cdot ))\) ( p 1 ( x , · ) , p 2 ( x , · ) ) -Laplacian problems with Dirichlet boundary conditions. Working within the framework of fractional Sobolev spaces with variable exponents, we apply the three critical points theorem as our key analytical tool to establish our main results. Under appropriate assumptions, we prove the existence of at least three distinct solutions for the considered problem.