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
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