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<p>We investigate a differential equation governed by the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Hilfer derivative and the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varrho (\cdot )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϱ</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian operator with Dirichlet boundary conditions involving two parameters. The nonlinearity of the problem, in general, does not satisfy the Ambrosetti–Rabinowitz type condition. By employing the topological degree for pseudomonotone operators within a variational approach, we establish the existence of positive solutions for a nonlinear Kirchhoff problem in suitable fractional <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Hilfer spaces.</p>

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Analysis of two-parameter capillarity Kirchhoff problem with \(\varrho (\cdot )\)-Laplacian operator by topology degree

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  • 出版模式：

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  • 发表日期：

    2026年7月25日

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  • Arhrrabi Elhoussain,
  • El-Houari Hamza,
  • Leandro S. Tavares

摘要

We investigate a differential equation governed by the \(\psi \) ψ -Hilfer derivative and the \(\varrho (\cdot )\) ϱ ( · ) -Laplacian operator with Dirichlet boundary conditions involving two parameters. The nonlinearity of the problem, in general, does not satisfy the Ambrosetti–Rabinowitz type condition. By employing the topological degree for pseudomonotone operators within a variational approach, we establish the existence of positive solutions for a nonlinear Kirchhoff problem in suitable fractional \(\psi \) ψ -Hilfer spaces.