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Zeitschrift für Analysis und ihre Anwendungen


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Volume 31, Issue 2, 2012, pp. 237–250
DOI: 10.4171/ZAA/1457

Published online: 2012-03-30

Optimal Control Problem of Positive Solutions to Second Order Impulsive Differential Equations

Lingling Zhang[1], Noriaki Yamazaki[2] and Chengbo Zhai[3]

(1) Taiyuan University of Technology, China
(2) Kanagawa University, Japan
(3) ShanXi University, Taiyuan, China

In this paper, we consider optimal control problem of second order impulsive differential equations. We show the existence and uniqueness of positive solutions to our problem for each given control functions. Also, we consider the control problem of positive solutions to our equations. Then, we prove the existence of an optimal control that minimizes the nonlinear cost functional. Moreover we give an example of the main results.

Keywords: Positive solutions, second order impulsive differential equations, fixed point theorem, optimal control problem

Zhang Lingling, Yamazaki Noriaki, Zhai Chengbo: Optimal Control Problem of Positive Solutions to Second Order Impulsive Differential Equations. Z. Anal. Anwend. 31 (2012), 237-250. doi: 10.4171/ZAA/1457