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<p>In this article, we focus on a class of degenerate Kirchhoff-type problems involving the discrete fractional <i>p</i>-Laplace operator. In the sublinear case, by applying Kajikiya’s symmetric mountain pass lemma, we establish the existence of infinitely many solutions with the corresponding critical values tending to 0 for a appropriate range of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1933_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>. In the superlinear case, the existence of infinitely many solutions is achieved through the classical symmetric mountain pass lemma. The primary characteristic and difficulty for our problems is that the Kirchhoff coefficient vanishes at zero, which means that the issue is degenerate. As far as we know, our results are novel in the context of the discrete fractional Laplacian.</p>

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Infinitely Many Solutions for Degenerate Kirchhoff-Type Problems Involving Discrete Fractional p-Laplacian

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Tianheng Song,
  • Lifeng Guo,
  • Binlin Zhang

摘要

In this article, we focus on a class of degenerate Kirchhoff-type problems involving the discrete fractional p-Laplace operator. In the sublinear case, by applying Kajikiya’s symmetric mountain pass lemma, we establish the existence of infinitely many solutions with the corresponding critical values tending to 0 for a appropriate range of \(\lambda \) λ . In the superlinear case, the existence of infinitely many solutions is achieved through the classical symmetric mountain pass lemma. The primary characteristic and difficulty for our problems is that the Kirchhoff coefficient vanishes at zero, which means that the issue is degenerate. As far as we know, our results are novel in the context of the discrete fractional Laplacian.