一类具有高阶奇性解的Hilbert核奇异积分方程(英文)

ON A CLASS OF SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL HAVING SOLUTIONS WITH SINGULARITY OF HIGH ORDER

本文利用指数变换研究了一类解具高阶奇性的周期黎曼边值问题,通过转化法研究了一类解具有高阶奇性的Hilber核奇异积分方程,获得了相应的解和可解条件表达式.推广了Hilber核奇异积分方程的结果.

In this paper, we discuss a class of Periodic Riemann boundary value problems which have solutions with high order singulary. The solutions and solvable conditions are given. Then on this base,the solutions and solvable conditions for a class of singular integral equations with Hilbert kernel which have solutions with the similar property are given. Thus we generalize the results about singular integral equations with Hilbert kernel.