Positive solutions for impulsive differential equations with mixed monotonicity and optimal control
type: Item
instance of: scholarly article
title: Positive solutions for impulsive differential equations with mixed monotonicity and optimal control
zbMATH Open document ID: 1469.34045
DOI: 10.1155/2014/974968
author: Noriaki Yamazaki
author: Rui Guo
author: Lingling Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider positive solutions and optimal control problem for a second order impulsive differential equation with mixed monotone terms. Firstly, by using a fixed point theorem of mixed monotone operator, we study positive solutions of the boundary value problem for impulsive differential equations with mixed monotone terms, and sufficient conditions for existence and uniqueness of positive solutions will be established. Also, we study positive solutions of the initial value problem for our system. Moreover, we investigate the control problem of positive solutions to our equations, and then, we prove the existence of an optimal control and its stability. In addition, related examples will be given for illustrations.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 49J21
zbMATH DE Number: 7023435
Wikidata QID: Q59043244
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/974968
OpenAlex ID: W2029555413
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description: scientific article; zbMATH DE number 7023435