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<p>In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2063_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\gamma (\tau ) $</EquationSource> </InlineEquation>-type triharmonic operator and Hardy potential. The main objective of this study is to establish the existence of entropy solutions for this problem under well-structured assumptions. Our approach relies on a novel analytical framework incorporating regularization techniques to handle the non-coercive nature of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2063_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\gamma (\tau ) $</EquationSource> </InlineEquation>-triharmonic operator in Sobolev spaces with variable exponent growth conditions. Additionally, we address the singularities arising from nonlinear source terms.</p>

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Existence results for \(\gamma (\tau )\)-triharmonic equation involving Navier boundary conditions and Hardy potential

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月14日

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  • Abdelaziz Sabiry,
  • Salah Boulaaras,
  • Ali El Mfadel,
  • Rafik Guefaifia

摘要

In this paper, we study the existence of weak solutions for a nonlinear elliptic Navier boundary value problem involving the γ ( τ ) $\gamma (\tau ) $ -type triharmonic operator and Hardy potential. The main objective of this study is to establish the existence of entropy solutions for this problem under well-structured assumptions. Our approach relies on a novel analytical framework incorporating regularization techniques to handle the non-coercive nature of the γ ( τ ) $\gamma (\tau ) $ -triharmonic operator in Sobolev spaces with variable exponent growth conditions. Additionally, we address the singularities arising from nonlinear source terms.