广义Hammerstain型非线性奇异积分方程的可解性定理

The Solvability of the Generalized Hammerstain Nonlinear Singular Integral Equations

本文所讨论的广义Hammerstain型非线性奇异积分方程:(*)是以流体弹性力学和断裂力学的边值问题为背景。我们分别对k>0,k=0,k<0这三种情况研究了方程(＊)的可解性,用Newton-Kantorovic方法和Banach不动点原理证明了方程(*)在不同条件下解的存在唯一性定理,从而推广了的工作。

The generalized Hammerstain nonlinear singular integral equation arising from the boundary value problems of fluid elastic mechanics and fracture mechanics:is studied in this paper. The solvability of equation for k>0, k = 0, k<0 respectively is studied and the existence and uniqueness of solutions of equationare proved under different conditions by using Newton-Kantorovic method and Ba-nach fixed point theorem. These results extend Γyceйнов's work.