Given is a nonlinear non-homogeneous polyanalytic differential equation of order in a simply-connected domain in the complex plane. Initially we prove (under certain conditions) the existence of its general solution in by first transforming it into a system of integro-differential equations. Next we prove the solvability of a generalized Riemann-Hilbert problem for the differential equation. This is effected by first reducing the boundary value problem posed to a corresponding one for a polyanalytic function. The latter is then transformed into classical Riemann-Hilbert problems for holomorphic functions, whose solutions are known in the literature.
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Ali Seif Mshimba, The Generalized Riemann-Hilbert Boundary Value Problem for Non-Homogeneous Polyanalytic Differential Equation of Order in the Sobolev Space . Z. Anal. Anwend. 18 (1999), no. 3, pp. 611–624DOI 10.4171/ZAA/901