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<p>This paper studies an anisotropic singular problem driven by <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44426_2025_19_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">\((\overset{\rightarrow }{p}(\cdot ),\overset{\rightarrow }{q}(\cdot ))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mover> <mi>q</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian operator with the variable strong-singularity and the variable Hardy-type potential. As the main machinery, the Ekeland’s variational principle and constrained minimization are applied to obtain the existence and uniqueness of a positive solution. An application is provided to illustrate the main result.</p>

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Anisotropic singular equation with \((\overset{\rightarrow }{p}(\cdot ),\overset{\rightarrow }{q}(\cdot ))\)-Laplacian operator and Hardy-type potential

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Mustafa Avci

摘要

This paper studies an anisotropic singular problem driven by \((\overset{\rightarrow }{p}(\cdot ),\overset{\rightarrow }{q}(\cdot ))\) ( p → ( · ) , q → ( · ) ) -Laplacian operator with the variable strong-singularity and the variable Hardy-type potential. As the main machinery, the Ekeland’s variational principle and constrained minimization are applied to obtain the existence and uniqueness of a positive solution. An application is provided to illustrate the main result.