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Existence, Uniqueness and UHR Stability of Solutions to Nonlinear Ordinary Differential Equations with Noninstantaneous Impulses

  • Xuping Zhang EMAIL logo and Zhen Xin
Published/Copyright: October 22, 2019

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 gi 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.

MSC 2010: 35A01; 35F25; 37C75

Acknowledgements

Research supported by NNSFs of China (11501455, 11661071), Doctoral Research Fund of Northwest Normal University (6014/0002020209) and Postgraduate Training and Curriculum Reform Project of Northwest Normal University (2018KGLX01014).

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Received: 2018-12-10
Accepted: 2019-09-30
Published Online: 2019-10-22
Published in Print: 2020-04-26

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