Banach空间中含非瞬时脉冲常微分方程解的存在性

Existence of Solutions for Ordinary Differential Equations with Non-instantaneous Impulses in Banach Space

利用k-集压缩映射不动点定理和新的非紧性测度估计,证明非瞬时脉冲常微分方程初值问题解的存在性,进而得到在非线性项满足较弱增长条件和非紧性测度条件,及非瞬时脉冲函数满足Lipschitz条件的假设下,非瞬时脉冲常微分方程初值问题解的存在性.

By using the fixed point theorem of k-set-contraction mapping and a new estimation of the measure of noncompactness,we proved the existence of the solution for the initial value problem of ordinary differential equations with non-instantaneous impulses,and then obtained the existence of the solution for the initial value problem of ordinary differential equations with non-instantaneous impulses under the assumption that the nonlinear term satisfied some weaker growth condition and noncompactness measure condition,and the non-instantaneous impulsive functions satisfied some Lipschitz conditions.