变积分限Cauchy核与卷积核混合的完全奇异积分方程的求解  

Solution of Complete Singular Integral Equation with Cauchy and Convolution Kernels and Variable Limit

作　　者：冯志新[1] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《吉林大学学报（理学版）》2013年第6期1051-1057,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11301215);吉林省自然科学基金(批准号:201215220)

摘　　要：考虑{0}函数类中,变积分限的Cauchy核与卷积核混合的完全奇异积分方程的求解问题,借助Fourier积分变换,利用Riemann边值问题和Fredholm积分方程理论,先将所讨论的方程转化为在一定可解条件下与其等价的{{0}}类中的Fredholm积分方程,再通过求解等价的Fredholm积分方程,得到所研究方程在{0}函数类中的可解条件及一般解.We discussed the solution of complete singular integral equation with Cauchy and convolution kernels and variable limit.Based on the Fourier transform and the theory of Riemann boundary value problem and Fredholm integral equation,the equation was transfered to the equivalent Fredholm integral equation in {{0}} undering some conditions.Then solving the equivalent Fredholm integral equation,we got solvable conditions and general solution on the equation discussed in { { 0 } }.

关 键 词：奇异积分方程 卷积核 CAUCHY核 FREDHOLM积分方程 

分 类 号：O175.6[理学—数学]