Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse
By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutra...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/592513 |
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| author | Zhenguo Luo Liping Luo Yunhui Zeng |
| author_facet | Zhenguo Luo Liping Luo Yunhui Zeng |
| author_sort | Zhenguo Luo |
| collection | DOAJ |
| description | By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))], t≠tk, k∈Z+; x(tk+)=x(tk-)+θk(x(tk)), k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained. |
| format | Article |
| id | doaj-art-62a77299b1904ec6b06daff22e8952b2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-62a77299b1904ec6b06daff22e8952b22025-02-03T06:06:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/592513592513Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and ImpulseZhenguo Luo0Liping Luo1Yunhui Zeng2Department of Mathematics, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, Hengyang Normal University, Hengyang 421008, ChinaDepartment of Mathematics, Hengyang Normal University, Hengyang 421008, ChinaBy using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))], t≠tk, k∈Z+; x(tk+)=x(tk-)+θk(x(tk)), k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.http://dx.doi.org/10.1155/2014/592513 |
| spellingShingle | Zhenguo Luo Liping Luo Yunhui Zeng Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse Journal of Applied Mathematics |
| title | Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse |
| title_full | Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse |
| title_fullStr | Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse |
| title_full_unstemmed | Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse |
| title_short | Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse |
| title_sort | positive periodic solution for the generalized neutral differential equation with multiple delays and impulse |
| url | http://dx.doi.org/10.1155/2014/592513 |
| work_keys_str_mv | AT zhenguoluo positiveperiodicsolutionforthegeneralizedneutraldifferentialequationwithmultipledelaysandimpulse AT lipingluo positiveperiodicsolutionforthegeneralizedneutraldifferentialequationwithmultipledelaysandimpulse AT yunhuizeng positiveperiodicsolutionforthegeneralizedneutraldifferentialequationwithmultipledelaysandimpulse |