2 problems

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Kolokolnikov–Ward conjecture on stability for the nonlocal eigenvalue problem
Kolokolnikov–Ward conjecture. For $r>1$ , if $\alpha>1$ , the spectrum of this nonlocal eigenvalue problem contains no eigenvalue with positive real part.
Conjectureopennonlocal-eigenvalue-problems reaction-diffusion stabilityarXiv posted 2 days ago
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Stability conjecture for the shifted NLEP above the critical parameter
Shifted NLEP stability conjecture. The shifted NLEP is stable for all $\mu>\mu_c(y_0)$ .
Conjectureopennonlocal-eigenvalue-problems reaction-diffusion-systems stability-analysisarXiv posted 2 days ago

Kolokolnikov–Ward conjecture on stability for the nonlocal eigenvalue problem