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

作　　者：钟寿国[1] 张如权[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2006年第3期257-261,共5页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助项目(14071107)

摘　　要：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.

关 键 词：非线性 周期Riemann边值问题 奇异积分方程 附加条件 

分 类 号：O175.8[理学—数学]