一类含Hilbert核非线性奇异积分方程的解法

On the Method of Solution for a Kind of Nonlinear Singular Integral Equation with Hilbert Kernel

首先提出在封闭光滑曲线上一类带平方根的周期Riemann问题并给出解和可解条件,然后将一类含Hilbert核非线性奇异积分方程转化为前者,得到封闭解及可解条件.作为本文特殊现象讨论了因Hilbert核积分性质所产生的附加条件的作用.

A kind of periodic Riemann boundary value problem with square roots on smooth closed contour is posed and its solution and solvable conditions are given. Then, a kind of nonlinear singular integral equation with Hilbert kernel is transformed to the former whose solution in closed form as well as its condition of solvability is obtained. For a special phenomenon in this paper,the cause and the actions of the ad ditional conditions produced by properties of integral with Hilbert kernel are discussed.