On continuous solutions of a generalized Cauchy– Riemann system with more than one singularity

We study the solvability of the Riemann–Hilbert problem for a generalized Cauchy–Riemann system with several singularities and reveal several new phenomenon. For the number of continuous solutions we shall show that it depends not only on the index but also on the location and type of the singularities; moreover, it does not depend continuously on the coefficients of the equation.