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

Article type: Research Article

Authors: Atkinson, F.V. | Peletier, L.A. | Serrin, J.

Affiliations: Department of Mathematics, University of Toronto, Toronto M5S 1A1, Ontario, Canada | Mathematical Institute, Leiden University, Leiden, The Netherlands | School of Mathematics, University of Minnesota, Minneapolis, MN, USA

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.

DOI: 10.3233/ASY-1992-5401

Journal: Asymptotic Analysis, vol. 5, no. 4, pp. 283-310, 1992