一类含卷积核与Cauchy核的奇异积分微分方程的非正则型解法  

A SOLUTION METHOD OF NON-NORMAL TYPE FOR ONE KIND OF SINGULAR INTEGRAL DIFFERENTIAL EQUATIONS WITH BOTH CONVOLUTION KERNEL AND CAUCHY KERNEL

作　　者：李平润[1,2] 

机构地区：[1]中国科学技术大学数学科学学院,合肥230026 [2]曲阜师范大学数学科学学院,曲阜273165

出　　处：《系统科学与数学》2014年第3期352-361,共10页Journal of Systems Science and Mathematical Sciences

基　　金：曲阜师范大学校青年基金(XJ201218)资助项目

摘　　要：提出并讨论了一类含卷积核与Cauchy核混合的奇异积分微分方程,通过运用Fourier变换,把此类奇异积分微分方程转化为Riemann边值问题,对此类边值问题运用与经典的Riemann边值问题不同的解法,讨论了非正则型情况,在函数类{0}中得到了方程的解与可解条件,特别对解在结点的性态进行了讨论.In this paper, we consider a kind of singular integral different equations with both convolution kernel and Cauchy kernel, which will be turned into Riemann boundary value problems by using the Fourier transform. Compared with the classical method for solution, we give another method. Therefore, the general solution and condition of solvability in class the function {0} are obtained in the non-normal type case. Especially, the behavior of the node of the equation is discussed.

关 键 词：卷积核 CAUCHY核 奇异积分微分方程 非正则型 

分 类 号：O175.6[理学—数学]