讨论了有序Banach空间$E$中的非线性常微分方程：$u^{\prime }(t)+Mu(t)=f(t,u(t)),\mathrm{\forall }t\in \mathbb{R}$ 正~$\omega$-周期解的存在性，其中$f:\mathbb{R}\times \to P$连续, $P$为$E$中的正元锥.通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正~$\omega$-周期解的存在性结果.

The existence of positive !-periodic solutions for order differential equations u′(t) + Mu(t) = f(t, u(t)), ∀ t ∈ R in an ordered Banach spaces E is discussed, where f : R × P → P is continuous, and P is the cone of positive elements in E. An existence result of positive !-periodic solutions is obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.