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<p>In the framework of saddle point reduction, we established a connection between the Maslov index of solutions to boundary value problems for Hamiltonian systems on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_267_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\([0, \infty )\)</EquationSource> </InlineEquation> and the Morse index of the corresponding functional defined through saddle point reduction. As an application, we demonstrated that boundary value problems for Hamiltonian systems on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_267_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\([0, \infty )\)</EquationSource> </InlineEquation> admit at least two nontrivial connecting orbits, utilizing the Morse index formula, saddle point reduction, and the three critical points theorem.</p>

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The Morse Index Theorem of Saddle Point Reduction and Applications to the Boundary Value Problems of Hamiltonian Systems on the Half Line

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月24日

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  • Ran Yang,
  • Qin Xing

摘要

In the framework of saddle point reduction, we established a connection between the Maslov index of solutions to boundary value problems for Hamiltonian systems on \([0, \infty )\) and the Morse index of the corresponding functional defined through saddle point reduction. As an application, we demonstrated that boundary value problems for Hamiltonian systems on \([0, \infty )\) admit at least two nontrivial connecting orbits, utilizing the Morse index formula, saddle point reduction, and the three critical points theorem.