Abstract and Applied Analysis
Volume 2006 (2006), Article ID 93163, 10 pages
doi:10.1155/AAA/2006/93163

An H-system for a revolution surface without boundary

P. Amster,1,2 P. De Nápoli,1,2 and M. C. Mariani3

1FCEyN, Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires 1428, Argentina
2Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
3Department of Mathematical Sciences, New Mexico State University Las Cruces, 88003-8001, NM, USA

Received 20 November 2003; Accepted 25 April 2005

Copyright © 2006 P. Amster et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence of solutions an H-system for a revolution surface without boundary for H depending on the radius f. Under suitable conditions we prove that the existence of a solution is equivalent to the solvability of a scalar equation N(a)=L/2, where N:𝒜⊂ℝ+→ℝ is a function depending on H. Moreover, using the method of upper and lower solutions we prove existence results for some particular examples. In particular, applying a diagonal argument we prove the existence of unbounded surfaces with prescribed H.