Abstract We consider the existence, uniqueness and Ulam–Hyers–Rassias stability of solutions to the initial value problem with noninstantaneous impulses on ordered Banach spaces. The existence and uniqueness of solutions for nonlinear ordinary differential equation with noninstantaneous impulses is obtained by using perturbation technique, monotone iterative method and a new estimation technique of the measure of noncompactness under the situation that the corresponding noninstantaneous impulsive functions g i are compact and not compact, respectively. Furthermore, the UHR stability of solutions is also obtained, which provides an approach to find approximate solution to noninstantaneous impulsive equations in the sense of UHR stability.

中文翻译：

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非瞬时脉冲非线性常微分方程解的存在性、唯一性和UHR稳定性

摘要 我们考虑了在有序 Banach 空间上具有非瞬时脉冲的初值问题解的存在性、唯一性和 Ulam-Hyers-Rassias 稳定性。利用微扰技术、单调迭代法和一种新的非紧性测度估计技术，在对应的非瞬时脉冲函数gi紧和不紧的情况下，得到了具有非瞬时脉冲的非线性常微分方程解的存在唯一性，分别。此外，还获得了解的UHR稳定性，这为从UHR稳定性的意义上寻找非瞬时脉冲方程的近似解提供了一种方法。