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<p>We show that there exists a ground state solution for a generalized Kadomtsev–Petviashvili equation in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_470_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. We prove that the ground state solution has energy equal to the mountain pass level of the functional corresponding to the equation.</p>

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On the energy of the ground state solution for a generalized Kadomtsev–Petviashvili equation

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Claudianor O. Alves,
  • Giovany M. Figueiredo,
  • Marcelo Montenegro

摘要

We show that there exists a ground state solution for a generalized Kadomtsev–Petviashvili equation in \(\mathbb {R}^2\) R 2 . We prove that the ground state solution has energy equal to the mountain pass level of the functional corresponding to the equation.