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<p>The objective of this study is to investigate the inhomogeneous nonlinear generalized Hartree equation within the mass-critical regime. Precisely, we give a threshold of global existence versus blow-up of energy solutions depending on the size of the mass compared with the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2107_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation> norm of the associated ground state. This complements the existing literature to the case of a non-local source term.</p>

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A note on the mass-critical inhomogeneous generalized Hartree equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月18日

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  • Saleh S. Almuthaybiri,
  • Tarek Saanouni

摘要

The objective of this study is to investigate the inhomogeneous nonlinear generalized Hartree equation within the mass-critical regime. Precisely, we give a threshold of global existence versus blow-up of energy solutions depending on the size of the mass compared with the L 2 $L^{2}$ norm of the associated ground state. This complements the existing literature to the case of a non-local source term.