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<p>We show that the principle “nonvanishing of spectral flow of the linearization along the trivial branch entails bifurcation of nontrivial solutions”, established in Fitzpatrick et al. (J Funct Anal 162:52–95, 1999) for critical points of one-parameter families of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1193_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> functionals with Fredholm Hessian, holds true for variational perturbations of paths of unbounded self-adjoint Fredholm operators as well.</p>

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Spectral flow and variational bifurcation

  • 期刊论文

  • 发表日期：

    2025年4月12日

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  • Jacobo Pejsachowicz

摘要

We show that the principle “nonvanishing of spectral flow of the linearization along the trivial branch entails bifurcation of nontrivial solutions”, established in Fitzpatrick et al. (J Funct Anal 162:52–95, 1999) for critical points of one-parameter families of \(C^2\) C 2 functionals with Fredholm Hessian, holds true for variational perturbations of paths of unbounded self-adjoint Fredholm operators as well.