二阶脉冲发展方程非局部问题mild解的存在性

Existence of mild solutions for the nonlocal problem of second-order impulsive evolution equations

首先通过引入一个Green函数,给出了含非局部条件n∑k=1C_(k)u(T_(k))的二阶非线性脉冲发展方程mild解的新定义。其次运用Sadovskii不动点定理证明了该mild解的存在性。最后,给出了一个具体例子作为抽象结果的应用。

A new definition of mild solutions of the second-order impulsive evolution equations involving nonlocal condition n∑k=1C_(k)u(T_(k))is given by introducing a Green function.Then,the existence of mild solutions of the concerned problem is proved by applying the Sadovskii fixed point theorem.At last,an example is provided as an application of the obtained abstract result.