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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |