<p>This paper delves into the existence of three weak solutions for a fractional <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_412_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\((\varphi , \psi )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>φ</mi> <mo>,</mo> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-like system involving the fractional <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_412_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> Laplacian and the fractional <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_412_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation> Laplacian respectively within the fractional Orlicz-Sobolev space. The proof is achieved by the well-known Bonanno-Marano techniques.</p>

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Multiplicity of couple solution for a fractional \((\varphi , \psi )\)-like system

  • Abderrahmane Lakhdari,
  • Chaima Nefzi

摘要

This paper delves into the existence of three weak solutions for a fractional \((\varphi , \psi )\) ( φ , ψ ) -like system involving the fractional \(\varphi \) φ Laplacian and the fractional \(\psi \) ψ Laplacian respectively within the fractional Orlicz-Sobolev space. The proof is achieved by the well-known Bonanno-Marano techniques.