An \(H\)-system for a revolution surface without boundary (Q2491421)

Summary: We study the existence of solutions of 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 \(N(a)={L}/{\sqrt{2}}\), where \(N:\mathcal{A}\subset \mathbb{R}^+\rightarrow \mathbb{R}\) 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 mean curvature \(H\).