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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Li, Pingrun¹ 

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

关键词: Singular integral-differential equations;    Riemann boundary value problems;    Convolution kernel;    Cauchy principal value integral;    Integral operators;   

DOI  :  10.1016/j.jmaa.2019.123643

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free