An H-system for a revolution surface without boundary. (2006) - Amster, P.; De Nápoli, P.; Mariani, M. C.
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 .