再生核空间中一类非线性积分方程的求解方法

The Methods for Solving a Class of Nonlinear Integral Equations

中文关键词:  再生核空间  线性算子方程  非线性积分方程

英文关键词:Reproducing kernel  linear operator equation  nonlinear integral equation.

中文摘要:

      本文在再生核空间中,利用再生核把非线性积分方程化为线性积分方程,研究了此类方程的求解问题,揭示了此类方程解的结构,存在性及多解等问题.

英文摘要:

      This paper deals with the problem for solving a class of nonlinear integral equations in reproducing kernel space W(Ω) . We use the reproducing kernel method to transform nonlinear integral equation K₁uK₂u+K₃u =f into a 2-dimension linear integral equation. We give also the factorization method and the characteristic value method to solve this nonlinear integral equation.