Non-normal type singular integral-differential equations by Riemann-Hilbert approach

Abstract

This article deals with one class of singular integral-differential equations of non-normal type with convolution and Cauchy principal value integral in class {0}. By using Fourier transform, this classes of equations are transformed into a Riemann boundary value problem with nodal point, and we prove the existence of solutions and the Noether theory for the equations. For such equations, we propose one method different from classical one, and we obtain the general solutions and the conditions of solvability. All cases about the behaviors of the solution are considered at nodal points. Therefore, the theory of integral equations and the classical Riemann boundary value problems is extended further.