Taiwanese Journal of Mathematics

Double Perturbations for Impulsive Differential Equations in Banach Spaces

Pengyu Chen, Yongxiang Li, and Xuping Zhang

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Abstract

In this article, we are concerned with the existence of extremal solutions to the initial value problem of impulsive differential equations in ordered Banach spaces. The existence and uniqueness theorem for the solution of the associated linear impulsive differential equation is established. With the aid of this theorem, the existence of minimal and maximal solutions for the initial value problem of nonlinear impulsive differential equations is obtained under the situation that the nonlinear term and impulsive functions are not monotone increasing by using perturbation methods and monotone iterative technique. The results obtained in this paper improve and extend some related results in abstract differential equations. An example is also given to illustrate the feasibility of our abstract results.

Article information

Source
Taiwanese J. Math., Volume 20, Number 5 (2016), 1065-1077.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874517

Digital Object Identifier
doi:10.11650/tjm.20.2016.5762

Mathematical Reviews number (MathSciNet)
MR3555889

Zentralblatt MATH identifier
1357.34100

Subjects
Primary: 34A37: Differential equations with impulses 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]

Keywords
initial value problem impulsive differential equation monotone iterative technique perturbation method measure of noncompactness

Citation

Chen, Pengyu; Li, Yongxiang; Zhang, Xuping. Double Perturbations for Impulsive Differential Equations in Banach Spaces. Taiwanese J. Math. 20 (2016), no. 5, 1065--1077. doi:10.11650/tjm.20.2016.5762. https://projecteuclid.org/euclid.twjm/1498874517


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