线性积分方程参数值的优化

The Optimization of Parameter on Linear Integral Equation

线性积分方程 φ(x) =f(x) +λ∫bak(x ,t) φ(t)dt中 ,λ的取值范围由 λ <1(b -a)maxx ,t k(x ,t) 拓广为λ <1maxx ∫ba k(x ,t)dt时仍有唯一解。当k(x ,t)可以分离为两函数H(x)与G(t)之积时 ,该方程解的一般形式为 :(x) =f(x) +αH(x) ,其中α为常数。

In the linear integral equation φ(x)=f(x)+λ∫b ak(x,t)φ(t)dt,when the scope of λ extends from λ<1 (b-a)maxx,tk(x,t) into λ<1maxx ∫b ak(x,t)dt, the above equation also has its only solution.If the function k(x,t) is split into the product of multiplification of H(x) and G(t),the general form of the solution to this equation is φ(x)=f(x)+αH(x),in which α is constant.