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Equivalence of min–max and max–min variational eigenvalue families

Determine whether the min–max and max–min variational eigenvalue sequences associated with the Krasnoselskii, Drábek, Yang, and $C^2$-spheres constructions (for $p>2$) coincide for all indices and parameters, or construct explicit counterexamples showing they differ.

References

Are they all the same or is there any example where they are different?

Nonlinear spectral graph theory (Deidda et al., 4 Apr 2025) in Subsection 3.2.4, Max-min Eigenvalues