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<p>Our paper is dedicated to studying the existence results of weak solutions in the variable exponents anisotropic Sobolev space with zero boundary <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44426_2025_9_Article_IEq1.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathring{W}^{1,\overrightarrow{p}(\cdot )}(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mover accent="true"> <mi>W</mi> <mo>˚</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover accent="true"> <mi>p</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of a boundary value problems for a class of anisotropic equations with variable exponents which generalizes the Kirchhoff-type equations.</p>

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Anisotropic equations with variable exponents for a class of generalized Kirchhoff-type equations

  • 期刊论文

  • 发表日期：

    2025年7月7日

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  • Mokhtar Naceri

摘要

Our paper is dedicated to studying the existence results of weak solutions in the variable exponents anisotropic Sobolev space with zero boundary \(\mathring{W}^{1,\overrightarrow{p}(\cdot )}(\Omega )\) W ˚ 1 , p → ( · ) ( Ω ) of a boundary value problems for a class of anisotropic equations with variable exponents which generalizes the Kirchhoff-type equations.