Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters
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: xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn...
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| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/214093 |
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| author | Zhenguo Luo |
| author_facet | Zhenguo Luo |
| author_sort | Zhenguo Luo |
| collection | DOAJ |
| description | 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: xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), i=1,2,…,n, k∈Z+, and xi′(t)=-ai(t)xi(t)+λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), 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. |
| format | Article |
| id | doaj-art-d774b3c7199941a5af63b9d5a59a5189 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d774b3c7199941a5af63b9d5a59a51892025-02-03T05:52:59ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/214093214093Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two ParametersZhenguo Luo0Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, ChinaBy 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: xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), i=1,2,…,n, k∈Z+, and xi′(t)=-ai(t)xi(t)+λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), 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.http://dx.doi.org/10.1155/2014/214093 |
| spellingShingle | Zhenguo Luo Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters Journal of Mathematics |
| title | Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters |
| title_full | Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters |
| title_fullStr | Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters |
| title_full_unstemmed | Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters |
| title_short | Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters |
| title_sort | multiple positive periodic solutions for two kinds of higher dimension impulsive differential equations with multiple delays and two parameters |
| url | http://dx.doi.org/10.1155/2014/214093 |
| work_keys_str_mv | AT zhenguoluo multiplepositiveperiodicsolutionsfortwokindsofhigherdimensionimpulsivedifferentialequationswithmultipledelaysandtwoparameters |