In this study we deal with the nonlinear Riemann--Hilbert problem (in short (RHP)) for generalized analytic functions in multiply connected domains. Using a similarity principle for multiply connected domains (presented here for the first time), we reduce the nonlinear RHP for generalized analytic functions to a corresponding nonlinear RHP for holomorphic functions with Hölder continuous boundary data. Then the Newton--Kantorovič method combined with a continuation procedure as well as a new existence theorem for holomorphic solutions, which is based on topological degree arguments, leads to existence of at least two topologically different generalized analytic functions solving the nonlinear RHP.
"Nonlinear Riemann-Hilbert Problems for Generalized Analytic Functions." Funct. Approx. Comment. Math. 40 (2) 185 - 208, June 2009. https://doi.org/10.7169/facm/1246454028