Double Perturbations for Impulsive Differential Equations in Banach Spaces

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 th...

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Published inTaiwanese journal of mathematics Vol. 20; no. 5; pp. 1065 - 1077
Main Authors Chen, Pengyu, Li, Yongxiang, Zhang, Xuping
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2016
Subjects
Abstract spaces
Banach space
Cauchy problem
Differential equations
Iterative methods
Mathematical constants
Mathematical functions
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Summary: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. 2010Mathematics Subject Classification. 34A37, 34K30. Key words and phrases. Initial value problem, Impulsive differential equation, Monotone iterative technique, Perturbation method, Measure of noncompactness.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.5762