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<p>This paper investigates multiplicity results for weak solutions to a degenerate weighted elliptic problem involving Leray-Lions operators, a Hardy-type potential, and a nonlocal source term that may exhibit singularities within the domain <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11868_2025_705_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mathscr {D} \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>. More precisely, we establish two main results. In the first, we employ critical point theory to demonstrate the existence of at least two distinct solutions in the superlinear case. In the second, we apply the variational method to prove the existence of three weak solutions in the sublinear case. These findings extend to a broad class of nonlinear problems in mathematical physics, addressing challenges related to degeneracy, Hardy-type singularities, and nonlocal interactions.</p>

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Existence results for variable exponents weighted quasilinear elliptic equations with degenerate Leray-Lions operators, indefinite nonlinearity, and Hardy-type term

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Khaled Kefi,
  • Abdeljabbar Ghanmi,
  • Mohamed El Ouaarabi

摘要

This paper investigates multiplicity results for weak solutions to a degenerate weighted elliptic problem involving Leray-Lions operators, a Hardy-type potential, and a nonlocal source term that may exhibit singularities within the domain \( \mathscr {D} \) D . More precisely, we establish two main results. In the first, we employ critical point theory to demonstrate the existence of at least two distinct solutions in the superlinear case. In the second, we apply the variational method to prove the existence of three weak solutions in the sublinear case. These findings extend to a broad class of nonlinear problems in mathematical physics, addressing challenges related to degeneracy, Hardy-type singularities, and nonlocal interactions.