A singularity-induced bifurcation theorem for infinite-dimensional implicit dynamical systems (Q2748080)

A class of partial differential equations whose formal structure resembles the semiexplicit, index-1 form from DAEs is considered. It is known from the theory on such problems, that one can encounter simple poles in the eigenvalue loci of parameter-dependent linearizations, leading to a loss of linear stability without the presence of steady-state bifurcations. Here, it is demonstrated how this phenomenon can be carried over to implicit problems defined on a Hilbert space.