Positive Periodic Solutions of Second-Order Differential Equations with Delays

Abstract

The existence results of positive ω-periodic solutions are obtained for the second-order differential equation with delays $-u^{″}+a(t)=f(t,u(t-{\tau }_1),\mathrm{...},u(t-{\tau }_n))$, where $a\in C(ℝ,(0,\infty ))$ is a ω-periodic function, $f:ℝ\times {[0,\infty )}^n\to [0,\infty )$ is a continuous function, which is ω-periodic in $t$, and ${\tau }_1,{\tau }_2,\mathrm{...},{\tau }_n$ are positive constants. Our discussion is based on the fixed point index theory in cones.