<p>In this paper, we investigate multiplicity results for a singular generalized <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2890_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Im \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℑ</mi> </math></EquationSource> </InlineEquation>-Hilfer double-phase Choquard fractional differential equation problems involving a <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2890_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak {p}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">p</mi> </math></EquationSource> </InlineEquation>-Laplacian operator with parameters and a nonlinear term exhibiting subcritical growth. Under broad assumptions on the data, we establish the existence of at least two weak positive solutions. Our approach relies on the fibering method, specifically utilizing the Nehari manifold. It is worth noting that our analysis encompasses both nondegenerate and degenerate Choquard cases. These findings contribute to the advancement of knowledge in the domain of double-phase Choquard issues within <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2890_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Im \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℑ</mi> </math></EquationSource> </InlineEquation>-Hilfer generalized fractional differential equations featuring singular non-linearity.</p>

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\(\Im \)-Hilfer Double Phase Choquard Problems with Singular Nonlinearity

  • El-Houari Hamza,
  • Arhrrabi Elhoussain,
  • Nemat Nyamoradi

摘要

In this paper, we investigate multiplicity results for a singular generalized \(\Im \) -Hilfer double-phase Choquard fractional differential equation problems involving a \(\mathfrak {p}\) p -Laplacian operator with parameters and a nonlinear term exhibiting subcritical growth. Under broad assumptions on the data, we establish the existence of at least two weak positive solutions. Our approach relies on the fibering method, specifically utilizing the Nehari manifold. It is worth noting that our analysis encompasses both nondegenerate and degenerate Choquard cases. These findings contribute to the advancement of knowledge in the domain of double-phase Choquard issues within \(\Im \) -Hilfer generalized fractional differential equations featuring singular non-linearity.