Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2013), Article ID 974968, 11 pages.
Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control
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.
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 974968, 11 pages.
First available in Project Euclid: 2 October 2014
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Zhang, Lingling; Yamazaki, Noriaki; Guo, Rui. Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 974968, 11 pages. doi:10.1155/2014/974968. https://projecteuclid.org/euclid.aaa/1412279716