In this paper the density of solutions of the operator equation y=y 0+LF(y)+LH(v) (L,H are linear operators and F is nonlinear) is discussed by Banach fixed point theorem and Schauder fixed point theorem, then by the gotten results the approximate controllability of the semilinear systemx′(t)+A(t)x(t)=f(t,x(t))+Bu(t)on Banach space is studied.
本文利用Ｂａｎａｃｈ不动点定理和Ｓｃｈａｕｄｅｒ不动点定理研究如下算子方程解的稠密性：ｙ＝ｙ０＋ＬＦ（ｙ）＋ＬＨ（ｖ）（其中，Ｌ、Ｈ为线性算子，Ｆ为非线性算子），然后，利用所得结论讨论Ｂａｎａｃｈ空间内的半线性系统：ｘ′（ｔ）＋Ａ（ｔ）ｘ（ｔ）＝ｆ（ｔ，ｘ（ｔ）＋Ｂｕ（ｔ）的近似可控