一类具有Hilbert核非正则型奇异积分方程的直接解法  

The Direct Method of Solution for a Class of Singular Integral Equation with Hilbert Kernel

作　　者：李凯雅 魏鑫 LI Kai-ya;WEI Xin(School of Science,Tianjin University of Technology and Education,Tianjin 300222,China;School of Science,Xi’an Shiyou University,Xi’an Shaanxi 710065,China)

机构地区：[1]天津职业技术师范大学理学院,天津300222 [2]西安石油大学理学院,陕西西安710065

出　　处：《菏泽学院学报》2020年第5期9-14,共6页Journal of Heze University

基　　金：西安石油大学助推计划(0108/134010029)。

摘　　要：遵循Cauchy核奇异积分方程直接解法的路线,研究带Hilbert核的奇异积分方程的直接解法.在不限于正则型,而允许在积分曲线上出现非正则型的单零点情况下,应用周期形式的推广的留数定理和推广的Plemelj公式得到奇异积分方程的解及可解条件.Following the route of direct solution of singular integral equation with Cauchy kernel,this paper studies the direct solution of singular integral equation with Hilbert kernel.In this paper,the solution and solvable condition of singular integral equation are obtained by using the generalized residue theorem of periodic form and the generalized Plemelj formula.

关 键 词：HILBERT核 非正则型 奇异积分方程 直接解法 

分 类 号：O175.5[理学—数学]