Solutions to $H$-systems by topological and iterative methods

Abstract

We study $H$-systems with a Dirichlet boundary data $g$. Under some conditions, we show that if the problem admits a solution for some $\left(H_0,g_0\right)$, then it can be solved for any $\left(H,g\right)$ close enough to $\left(H_0,g_0\right)$. Moreover, we construct a solution of the problem applying a Newton iteration.