Nonlinear Riemann-Hilbert problems for doubly connected domains and closed boundary data

Abstract

In this paper, for nonlinear Riemann–Hilbert problems in doubly connected domains with smooth as well as Lipschitz continuous boundary data, existence of at least two topologically different solutions is established. The main tools are the topological degree of quasi-ruled Fredholm mappings, Montel’s theorem, a priori estimates and the employment of classical modular function theory.