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<p>In this paper, we analyze a class of Dirichlet boundary value problems governed by nonlinear <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3242_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\((\alpha (z),\beta (z))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>β</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian operators in the framework of Musielak-Orlicz-Sobolev spaces with variable exponents. This approach offers a robust investigation into the existence of weak solutions for nonlinear systems characterized by variable growth conditions and nonlinearity. We leverage Young measures to effectively manage weak convergence and apply the Galerkin method to construct the solutions, ensuring a comprehensive understanding of the proposed problem.</p>

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Weak solutions of fractional double-phase Laplacian-like problems in variable exponent Musielak-Orlicz Sobolev spaces

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Hasna Moujani,
  • Ayoub Elhafiane,
  • Ali El Mfadel,
  • Abderrazak Kassidi,
  • M’hamed El Omari

摘要

In this paper, we analyze a class of Dirichlet boundary value problems governed by nonlinear \((\alpha (z),\beta (z))\) ( α ( z ) , β ( z ) ) -Laplacian operators in the framework of Musielak-Orlicz-Sobolev spaces with variable exponents. This approach offers a robust investigation into the existence of weak solutions for nonlinear systems characterized by variable growth conditions and nonlinearity. We leverage Young measures to effectively manage weak convergence and apply the Galerkin method to construct the solutions, ensuring a comprehensive understanding of the proposed problem.