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<p>We study the existence and asymptotic behavior of normalized ground states for the nonlinear fractional energy critical Kirchhoff equation with mass critical and supercritical perturbations in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3308_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="96" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^N(N=2,3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. The presence of the fractional energy critical exponent in the Kirchhoff nonlocal setting makes the problem more challenging, as the underlying fractional order algebraic equation cannot be solved precisely. To address this challenge, we establish the threshold energy estimates based on the monotonicity trick and truncation technique. By combining the minimax procedure and Pohožaev manifold decomposition, we prove the existence of the normalized ground states. Moreover, we also explore the asymptotic behavior of the normalized ground states.</p>

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Normalized ground states for fractional energy critical Kirchhoff equations with the mass critical and supercritical perturbations

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Lingzheng Kong,
  • Liyan Zhu,
  • Haibo Chen

摘要

We study the existence and asymptotic behavior of normalized ground states for the nonlinear fractional energy critical Kirchhoff equation with mass critical and supercritical perturbations in \(\mathbb {R}^N(N=2,3)\) R N ( N = 2 , 3 ) . The presence of the fractional energy critical exponent in the Kirchhoff nonlocal setting makes the problem more challenging, as the underlying fractional order algebraic equation cannot be solved precisely. To address this challenge, we establish the threshold energy estimates based on the monotonicity trick and truncation technique. By combining the minimax procedure and Pohožaev manifold decomposition, we prove the existence of the normalized ground states. Moreover, we also explore the asymptotic behavior of the normalized ground states.