【摘要】 利用强连续余弦族理论和Schauder不动点定理给出了下列二阶非线性微分方程可控性的充分性条件.x″(t)=Ax(t)+f(t,x(t))+Bu(t),t∈I=[0,T],x(0)=x0,x′(0)=y0.在文中,考虑了其阻尼项x′(.),使得对任意的x0,y0∈x,系统解满足x(T)=x′和x′(T)=y′,并且推广了文[1]中的相关结论.更多还原

【Abstract】 A sufficient conditions for the controllability of the following nonlinear second order differential equations is given by using the theory of strongly continuous cosine families and Schauder fixed-point theorem,x″(t)=Ax(t)+f(t,x(t))+Bu(t),t∈I=,x(0)=x0,x′(0)=y0.We consider the damping term x′(·) so that the solution of the system satisfies x(T)=x′ and x(T)=y′ for all x0,y0∈x.Our result extend the corresponding results of [1].更多还原