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<p>In this paper, we investigate fractional double-phase problems involving Kirchhoff-type operators and variable exponents. Specifically, we address problems incorporating Lipschitz continuous functions, compactness, and variable exponents, using both the fiber method and the Nehari manifold within fractional spaces. The study focuses on a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ψ</mi> </math></EquationSource> </InlineEquation>-Hilfer fractional operator, integrating variable exponents and derivatives. Conducted within the context of Sobolev and Banach spaces with variable exponents, this work considers Dirichlet-type limit conditions for a boundary value problem involving the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p(\cdot )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Kirchhoff-type operator and establishes the existence of multiple weak solutions.</p>

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Fractional double-phase problems with Kirchhoff-type operators and variable exponents

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Mohamed El Khayr Boukraa,
  • Mohamed Saad Bouh Elemine Vall

摘要

In this paper, we investigate fractional double-phase problems involving Kirchhoff-type operators and variable exponents. Specifically, we address problems incorporating Lipschitz continuous functions, compactness, and variable exponents, using both the fiber method and the Nehari manifold within fractional spaces. The study focuses on a \(\Psi \) Ψ -Hilfer fractional operator, integrating variable exponents and derivatives. Conducted within the context of Sobolev and Banach spaces with variable exponents, this work considers Dirichlet-type limit conditions for a boundary value problem involving the \(p(\cdot )\) p ( · ) -Kirchhoff-type operator and establishes the existence of multiple weak solutions.