含参数的一类非线性算子方程解对参数的连续相依性定理及应用

Continuous Dependence Theorem of Solutions for a Class of Nonlinear Equations on a Parameter and Applications

该文利用锥理论和 Banach压缩映象原理讨论了一类含参数的非线性算子方程 ,证明了这类方程解的存在唯一性及其解对参数的连续相依性定理 ,并给出了对 Banach空间中含参数的一阶积

This paper discusses a class of nonlinear equation with a parameter by means of the cone theory and Banach contraction mapping principle, it is proved that the existence and uniqueness of solutions for this kind equations and continuous dependence of solutions on the parameter. The results obtained in this paper are applied to the initial value problem for first order integro differential equations of mixed type in Banach spaces.