一类积分微分包含的可控体

Controllability of integrodifferential inclusions

研究了一类带有非局部条件积分微分包含的可控性,在多值函数F(t,x)取凸和非凸两种情形下讨论了上述问题,建立了可控性的充分条件．对于凸情形,将所讨论的问题转化为集值积分算子的不动点问题,利用Kakutani不动点定理得到可控性．对于非凸情形,将所讨论的问题转化为单值积分算子的不动点问题,利用Schauder不动点定理得到可控性．

Controllability problems of integrodifferential inclusion with nonlocal conditions have been researched. We consider this problem and establish sufficient conditions for both convex and nonconvex multi- function F（t,x）. For convex case, the problem is converted into fixed pointed problem of set-valued integral operators, then the controllability theorem is obtained by using Kakutani fixed point theorem. For nonconvex case, the problem is converted into fixed pointed problem of single-valued integral operators, then the desired result is obtained by using Schauder fixed point theorem.