Abstract and Applied Analysis

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

Qiang Li and Yongxiang Li

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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 τ 1 ( t ) ) , , u ( t τ n ( t ) ) ) , where a ( t ) C ( ) is a positive ω-periodic function, f : × [ 0 , + ) n + 1 [ 0 , + ) is a continuous function which is ω-periodic in t, and τ 1 ( t ) , , τ n ( t ) C ( , [ 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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 929870, 13 pages.

Dates
First available in Project Euclid: 7 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1399486653

Digital Object Identifier
doi:10.1155/2012/929870

Mathematical Reviews number (MathSciNet)
MR3004880

Zentralblatt MATH identifier
1260.34136

Citation

Li, Qiang; Li, Yongxiang. On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 929870, 13 pages. doi:10.1155/2012/929870. https://projecteuclid.org/euclid.aaa/1399486653


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