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<p>Although a Fractional Picone’s inequality is already known for problems dealing with fractional <i>p</i>-Laplacian, one of its consequences is missing, the one usually used to prove the nonexistence of solutions. In this paper, we prove this result (see Theorem <InternalRef RefID="FPar2">1.2</InternalRef>) and, as a consequence, we deal with a fractional <i>p</i>-Laplacian problem with Dirichlet boundary conditions and a nonlinearity involving a supercritical exponential term. We also study the asymptotic behavior of its solutions as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_472_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\rightarrow 1^+\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">→</mo> <msup> <mn>1</mn> <mo>+</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_472_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\rightarrow \infty\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, which are related to the Cheeger constant and the distance function, respectively.</p>

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On a consequence of Picone’s identity for a fractional p-Laplacian

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • H. P. Bueno,
  • M. R. Marcial,
  • G. A. Pereira

摘要

Although a Fractional Picone’s inequality is already known for problems dealing with fractional p-Laplacian, one of its consequences is missing, the one usually used to prove the nonexistence of solutions. In this paper, we prove this result (see Theorem 1.2) and, as a consequence, we deal with a fractional p-Laplacian problem with Dirichlet boundary conditions and a nonlinearity involving a supercritical exponential term. We also study the asymptotic behavior of its solutions as \(p\rightarrow 1^+\) p → 1 + and \(p\rightarrow \infty\) p → ∞ , which are related to the Cheeger constant and the distance function, respectively.