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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/974968 |
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| _version_ | 1832556567211278336 |
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| author | Lingling Zhang Noriaki Yamazaki Rui Guo |
| author_facet | Lingling Zhang Noriaki Yamazaki Rui Guo |
| author_sort | Lingling Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-acefce82e36c4d65b53e5e4f1c296be8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-acefce82e36c4d65b53e5e4f1c296be82025-02-03T05:45:01ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/974968974968Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal ControlLingling Zhang0Noriaki Yamazaki1Rui Guo2Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaDepartment of Mathematics, Kanagawa University, Yokohama 221-8686, JapanDepartment of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaWe 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.http://dx.doi.org/10.1155/2014/974968 |
| spellingShingle | Lingling Zhang Noriaki Yamazaki Rui Guo Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control Abstract and Applied Analysis |
| title | Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control |
| title_full | Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control |
| title_fullStr | Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control |
| title_full_unstemmed | Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control |
| title_short | Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control |
| title_sort | positive solutions for impulsive differential equations with mixed monotonicity and optimal control |
| url | http://dx.doi.org/10.1155/2014/974968 |
| work_keys_str_mv | AT linglingzhang positivesolutionsforimpulsivedifferentialequationswithmixedmonotonicityandoptimalcontrol AT noriakiyamazaki positivesolutionsforimpulsivedifferentialequationswithmixedmonotonicityandoptimalcontrol AT ruiguo positivesolutionsforimpulsivedifferentialequationswithmixedmonotonicityandoptimalcontrol |