Local bifurcation structure and stability of charged drops

According to the range of dielectric coefficient [Formula: see text], we determine the shape and stability of charged drops. We first obtain a sequence of bifurcation points [Formula: see text] and bifurcation curves [Formula: see text]. Then we determine the stable or unstable ranges of the charged drop based on the local bifurcation structure. In particular, we give a confirmed answer to a conjecture proposed by Tsamopoulos et al.