一类含ζ核的奇异积分-微分方程的直接解法

A Direct Method of Solution for A Class of Singular Integro-Differential Equations with ξ Kernel

研究了一类含ζ核的奇异积分-微分方程.利用推广的Plemelj公式构造出一阶微分方程,通过求解该方程直接得出此类奇异积分-微分方程的解,从而给出了这样一类复杂方程的直接解法及其可解条件.

A class of singular integro-differential equations with ξ kernel under some analytic conditions is discussed.Making use of the generalized Plemelj formula,a first order differential equation is constructed.Then,the solution of the singular integro-differential equation can be easily obtained through solving this equation.So the direct method of solution for these very complicated equations are gained,and the soluble condition is also given.