Abstract and Applied Analysis

Positive Periodic Solutions of Third-Order Ordinary Differential Equations with Delays

Abstract

The existence results of positive $\omega$-periodic solutions are obtained for the third-order ordinary differential equation with delays ${u}^{\mathrm{\prime \prime \prime }}(t)+a(t)u(t)=f(t,u(t-{\tau }_{\mathrm{0}}),{u}^{\prime }(t-{\tau }_{\mathrm{1}}),{u}^{\mathrm{\prime \prime }}(t-{\tau }_{\mathrm{2}})),t\in \mathrm{\Bbb R,}$ where $a\in C(\Bbb R,(\mathrm{0},\infty ))$ is $\omega$-periodic function and $f:\Bbb R{\times}[0,\infty ){\times}{\Bbb R}^{2}\to [0,\infty )$ is a continuous function which is $\omega$-periodic in $t,\text{and\hspace\{0.17em\}}{\tau }_{\mathrm{0}},{\tau }_{\mathrm{1}},{\tau }_{\mathrm{2}}$ are positive constants. The discussion is based on the fixed-point index theory in cones.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 547683, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412273177

Digital Object Identifier
doi:10.1155/2014/547683

Mathematical Reviews number (MathSciNet)
MR3173281

Zentralblatt MATH identifier
07022602

Citation

Li, Yongxiang; Li, Qiang. Positive Periodic Solutions of Third-Order Ordinary Differential Equations with Delays. Abstr. Appl. Anal. 2014 (2014), Article ID 547683, 8 pages. doi:10.1155/2014/547683. https://projecteuclid.org/euclid.aaa/1412273177

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