Piecewise continuous mild solutions of a system governed by impulsive differential equations in locally convex spaces

Existence and uniqueness problems of piecewise continuous mild solutions for a system governed by impulsive differential equations in locally convex spaces are solved. The global existence problem is proved for the uniformly Lipschitz case while the local existence problem is proved for the locally Lipschitz case. A priori estimate is given and used as an important tool for proving the global existence of a mild solution. The continuous dependence on impulsive conditions of the system is also proved. Our main results are obtained by using the fixed point theorem of a seminorm contraction. Some examples are given.