ABSTRACT
We begin with the case of simple eigenvalues, where the calculus is rather straightforward. Actually, in the elliptic setting, this happens for l = 0 only, but, nevertheless, we perform the analysis for any l ≥ 0 bearing in mind some possible restrictions on the geometry of eigenfunctions (e.g., this happens for any l = 0, 1, 2, ... in the radial ODE setting). Since the nonlinear perturbation term in the integral equation (22) is an odd sufficiently smooth operator, we arrive at the following result describing the local behavior of bifurcation branches; see [251] and [252, Ch. 8].
