Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-06
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of n -dimension periodic impulsive functional differential equations with multiple delays and two parameters: x i ′ ( t ) = a i ( t ) x i ( t ) - λ b i ( t ) f i ( t , x ( t ) , x ( t - τ 1 ( t ) ) , … , x ( t - τ n ( t ) ) ) ), a.e., t > 0 , t ≠ t k , k ∈ Z + , x i ( t k + ) - x i ( t k - ) = μ c i k x i ( t k ) , i = 1,2 , … , n , k ∈ Z + , and x i ′ ( t ) = - a i ( t ) x i ( t ) + λ b i ( t ) f i ( t , x ( t ) , x ( t - τ 1 ( t ) ) , … , x ( t - τ n ( t ) ) ) ), a.e., t > 0 , t ≠ t k , k ∈ Z + , x i ( t k + ) - x i ( t k - ) = μ c i k x i ( t k ) , i = 1,2 , … , n , k ∈ Z + .
As an application, we study some special cases of the previous systems, which have been studied extensively in the literature.
American Psychological Association (APA)
Luo, Zhenguo. 2014. Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters. Journal of Mathematics،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1041066
Modern Language Association (MLA)
Luo, Zhenguo. Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters. Journal of Mathematics No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1041066
American Medical Association (AMA)
Luo, Zhenguo. Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters. Journal of Mathematics. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1041066
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1041066