On the Existence of Positive Periodic Solutions for Second‐Order Functional Differential Equations with Multiple Delays

Qiang Li and Yongxiang Li

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
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https://doi.org/10.1155/2012/929870

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:929870

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