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. Amster1
, P. De Nápoli1
and M.C. Mariani3
1FCEyN, Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires 1428, Argentina
3Department of Mathematical Sciences, New Mexico State University Las Cruces, 88003-8001, NM, USA
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.