An Iteration Method for Solving Elliptic Equations

Abstract

In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to unbounded domains, as we show with domains of the form $\mathbb{R}^{n-1}\times\left(-d/2,d/2\right)$.