Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System
In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions for n-dimensional nonautonomous functional differential system x'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), where hi are ω-periodic in t and there exist ω-periodic functions αi,βi∈C(R,R+) such that αi(t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/268418 |
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| author | Youjun Liu Huanhuan Zhao Jurang Yan |
| author_facet | Youjun Liu Huanhuan Zhao Jurang Yan |
| author_sort | Youjun Liu |
| collection | DOAJ |
| description | In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions for n-dimensional nonautonomous functional differential system x'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), where hi are ω-periodic in t and there exist ω-periodic functions αi,βi∈C(R,R+) such that αi(t)≤(hi(t,x)/xi)≤βi(t),∫0ωαi(t)dt>0, for x∈R+n all with xi>0, and t∈R, limxi→0+(hi(t,x)/xi) exist for t∈R; bi∈C(R,R+) are ω-periodic functions and ∫0ωbi(t)dt>0;fi∈C(R+n,R+), fi(x)>0 for x >0; τ∈(R,R) is an ω-periodic function. We show that the system has multiple or no positive ω-periodic solutions for sufficiently large or small λ>0, respectively. |
| format | Article |
| id | doaj-art-3ea947e95f794497a6f2947808d03964 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3ea947e95f794497a6f2947808d039642025-02-03T00:59:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/268418268418Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous SystemYoujun Liu0Huanhuan Zhao1Jurang Yan2College of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, ChinaCollege of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaIn this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions for n-dimensional nonautonomous functional differential system x'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), where hi are ω-periodic in t and there exist ω-periodic functions αi,βi∈C(R,R+) such that αi(t)≤(hi(t,x)/xi)≤βi(t),∫0ωαi(t)dt>0, for x∈R+n all with xi>0, and t∈R, limxi→0+(hi(t,x)/xi) exist for t∈R; bi∈C(R,R+) are ω-periodic functions and ∫0ωbi(t)dt>0;fi∈C(R+n,R+), fi(x)>0 for x >0; τ∈(R,R) is an ω-periodic function. We show that the system has multiple or no positive ω-periodic solutions for sufficiently large or small λ>0, respectively.http://dx.doi.org/10.1155/2014/268418 |
| spellingShingle | Youjun Liu Huanhuan Zhao Jurang Yan Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System Discrete Dynamics in Nature and Society |
| title | Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System |
| title_full | Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System |
| title_fullStr | Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System |
| title_full_unstemmed | Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System |
| title_short | Existence of Positive Periodic Solutions for n-Dimensional Nonautonomous System |
| title_sort | existence of positive periodic solutions for n dimensional nonautonomous system |
| url | http://dx.doi.org/10.1155/2014/268418 |
| work_keys_str_mv | AT youjunliu existenceofpositiveperiodicsolutionsforndimensionalnonautonomoussystem AT huanhuanzhao existenceofpositiveperiodicsolutionsforndimensionalnonautonomoussystem AT jurangyan existenceofpositiveperiodicsolutionsforndimensionalnonautonomoussystem |