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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6148393, 6 pages
https://doi.org/10.1155/2017/6148393
Research Article

Singular Integral Equations of Convolution Type with Cosecant Kernels and Periodic Coefficients

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Correspondence should be addressed to Pingrun Li

Received 15 July 2017; Revised 30 August 2017; Accepted 7 September 2017; Published 9 October 2017

Academic Editor: Elena Benvenuti

Copyright © 2017 Pingrun Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study singular integral equations of convolution type with cosecant kernels and periodic coefficients in class . Such equations are transformed into a discrete jump problem or a discrete system of linear algebraic equations by using discrete Fourier transform. The conditions of Noethericity and the explicit solutions are obtained by means of the theory of classical boundary value problem and of the Fourier analysis theory. This paper will be of great significance for the study of improving and developing complex analysis, integral equations, and boundary value problems.