Estimates for vertical points of solutions of prescribed mean curvature type equations II

Abstract

Radially symmetric solutions u(r) of the prescribed mean curvature equation involving a source term f(u) may exhibit vertical points. In this paper we study the asymptotic properties of these vertical points when f is positive and increasing and the parameter ε=f′/f² becomes small. Our results are based on a sharp asymptotic estimate for Delaunay surfaces as the distance of the vertical points nearest to the symmetry axis r=0 tends to zero.