Real analyticity and non-degeneracy

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Supercritical elliptic problems in domains with small holes (2007, background): “This fact is also in the background of Dancer’s proof to deal with the vanishing of u at the boundary in the proof of analyticity with respect to p.”
Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level (2005, background): “n = 2 and p is any odd integer larger than 2. It has been pointed out to us by Dancer that the map u �→ up is analytic for all p ∈ (1, n+2 n−2) when restricted to open subsets of the positive cone in a weighted space of continuous functions; see [ 11 ].”
Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus (2011, methodology): “It was proved by Dancer in [ 4 ]t hat ifp0 and u0 are such that there exists a μ> 0 for which u0 ≥ μϕ1 then the map”