一种带有奇异核的Volterra第二种积分方程的解

SOLUTION OF A VOLTERRA SINGULAR INTEGRAL EQUATION OF THE SECOND KIND

本文提供了一种解带有特定奇异核为1/(s-t)~a(0<a<1) 的 Volterra 第2种积分方程的方法。主要是通过对方程进行拉氏变换、函数的幂级数展开等过程,求得未知函数的拉氏变换表达式,然后对其进行反变换,即得所求函数。最后给出了此解的证明及 a=1/2的特例。

This paper presents a method for solving a volterra integral equation of the second kind with such a singular kernal as 1/(s-t)(?)(0<α<1) .First,the Laplace expression of the unknown function is obtained mainly by means of Laplace transform, asymptotic expansion etc.,then the unknown function via the inverse of Laplace trans- form can be got.Second,the aquired asymptotic solution is strictly proved for its cor- retness.Finally,a concrete example is given as α=1/2.