On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays
The existence results of positive ω-periodic solutions are obtained for the second-order functional differential equation with multiple delays u″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), where a(t)∈C(ℝ) is a positive ω-periodic function, f:ℝ×[0,+∞)n+1→[0,+∞) is a continuous function which is ω...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/929870 |
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| _version_ | 1832546576641294336 |
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| author | Qiang Li Yongxiang Li |
| author_facet | Qiang Li Yongxiang Li |
| author_sort | Qiang Li |
| collection | DOAJ |
| description | The existence results of positive ω-periodic solutions
are obtained for the second-order functional differential equation with
multiple delays u″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))),
where a(t)∈C(ℝ) is a positive ω-periodic function, f:ℝ×[0,+∞)n+1→[0,+∞) is a continuous function which is ω-periodic in t, and τ1(t),…,τn(t)∈C(ℝ,[0,+∞)) are ω-periodic functions. The existence conditions
concern the first eigenvalue of the associated linear periodic
boundary problem. Our discussion is based on the fixed-point index
theory in cones. |
| format | Article |
| id | doaj-art-08f9a10e6f6d4fad9e4f71098bbf707e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-08f9a10e6f6d4fad9e4f71098bbf707e2025-02-03T06:48:05ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/929870929870On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple DelaysQiang Li0Yongxiang Li1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaThe existence results of positive ω-periodic solutions are obtained for the second-order functional differential equation with multiple delays u″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), where a(t)∈C(ℝ) is a positive ω-periodic function, f:ℝ×[0,+∞)n+1→[0,+∞) is a continuous function which is ω-periodic in t, and τ1(t),…,τn(t)∈C(ℝ,[0,+∞)) are ω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.http://dx.doi.org/10.1155/2012/929870 |
| spellingShingle | Qiang Li Yongxiang Li On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays Abstract and Applied Analysis |
| title | On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays |
| title_full | On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays |
| title_fullStr | On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays |
| title_full_unstemmed | On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays |
| title_short | On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays |
| title_sort | on the existence of positive periodic solutions for second order functional differential equations with multiple delays |
| url | http://dx.doi.org/10.1155/2012/929870 |
| work_keys_str_mv | AT qiangli ontheexistenceofpositiveperiodicsolutionsforsecondorderfunctionaldifferentialequationswithmultipledelays AT yongxiangli ontheexistenceofpositiveperiodicsolutionsforsecondorderfunctionaldifferentialequationswithmultipledelays |