An H -system for a revolution surface without boundary (Abstract and Applied Analysis)
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 .