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<p>In the present paper we study a parametrized Kirchhoff type equation with two degeneracy points. The existence of two <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3118_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_0^1(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>H</mi> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-norm ordered solutions is established for small value of the parameter via a careful analysis of the fiber maps associated to the energy functional. As a consequence we show existence of multiple or even infinitely many solutions to degenerate Kirchhoff equations. Due to the simplicity of the conditions, many applications are given.</p>

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Ordered solutions for degenerate Kirchhoff problems

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • F. Faraci,
  • K. Silva

摘要

In the present paper we study a parametrized Kirchhoff type equation with two degeneracy points. The existence of two \(H_0^1(\Omega )\) H 0 1 ( Ω ) -norm ordered solutions is established for small value of the parameter via a careful analysis of the fiber maps associated to the energy functional. As a consequence we show existence of multiple or even infinitely many solutions to degenerate Kirchhoff equations. Due to the simplicity of the conditions, many applications are given.