一类非线性奇异积分方程的迭代解法

Iterative Method to Solve a Class of Nonlinear Singular Integral Equations

研究一类不含参数 λ的非线性奇异积分方程 u=Fu,并给出它的一种迭代解法 ,其中非线性算子 F可以分解为有限个算子之和 F= mi=1 Fi,且算子 Fi具有幂的性质 :Fi( au) =a Ki Fi( u) ( Ki<1 ) .

Differing from general nonlinear equations λ, a class of nonlinear singular integral equations u=Fu without parameter F is considered. The iterative solution is given when the nonlinear operator F can be decomposed into a finite sum F=? 苮mi=1F i, and the operator F i possesses the power property: F i(au)=a K i F i(u)(K i<1).