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This article deals with the solvability and explicit solutions of one class of singular integral equations with two convolution kernels in the non-normal type case. Via using techniques of complex analysis, such equations are transformed into Riemann–Hilbert boundary value problems (R-HPs) with the discontinuous property. We establish a regularity theory and existence of solutions, and obtain the general solutions and the conditions of Noether solvability. Especially, we investigate the asymptotic behaviours of solutions at nodes. Thus, this paper generalizes the theories of integral equations and Riemann–Hilbert boundary value problems.

An efficient method for singular integral equations of non-normal type with two convolution kernels